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["Missing","Dimension","Machine","Diameter","Switches","Account Manager","Sales","Reps","Marketing","Products","Speed","Valve","Temperature","Catalyst","Speed","Valve","Revenue","Month","Stained","Sampled","Response Time","Waiting Time","Parts","Subgroup","Approval Time","Dimension","Wood","Delivery Time","Boxcox","Unstable","Unresolved","Enquiries","Scratches","Pressure","Sleep Hours","Smoker","Lifespan","Pesticide","Humidity","Sports","Gender","Age","Measurement","Part","Operator","Readings","Samples","Reference","Part_Att","Reference_Att","Acceptances_Att","Rating","Garment","Controller","Standard","Wind","Material","BladeSize","Strength","Mix","Batch","Time","Measurement","Tire-A","Tire-B","Score","Sales A","Sales B","Cycle Time","Officer","Strength","Hardener","Batch","Interest","Count","Probability","Age","Chocolate","Strawberry","Vanilla","Response","Failure Times","Censor","Start","End","Frequency","Times","Temp","Cen","Times2","Cen2","Temp2","Chamber2"]
["Invoice number",12.66,"Machine1",300,1658,"John",2206245,90,39074.5,8,56.8,100,20,"A",90.1,100,52135,"2005-01-01",6,104,24,6.33,8.69,1,45,210.8,"G1",5,2.89,2.12,67,525,1,"Good",10,"No",1,7.2,"Low","Golf","Female",28,10.199999999999999,1,1,0.27,1,0.2,1,0.2,0,2,1,"Frances",2,65,"C",12,4.6500000000000004,1,1,9.6199999999999992,4.0599999999999996,10.3,10.6,20,54,61,45,"C",52,1,1,"Engineering",156,0.6,"<20",32,11,22,370.63,151,"F","*",100,5,313,140,"F",313,"F",28.09,"A"]
["Invoice number",12.53,"Machine1",302,1544,"John",1721959,63,30931.5,7,56.1,110,20,"A",121.5,110,52545,"2005-02-01",7,107,19,5.38,8.64,1,70,201.7,"G1",23,2.9,1.91,62,503,3,"Good",8,"No",3,4.5,"High","Tennis","Male",29,11.4,1,1,0.25,1,0.2,2,0.25,0,2,1,"Mary",2,123,"C",14,4.5999999999999996,1,1,8.25,3.93,9.1999999999999993,9.6,22,50,58,36,"B",46.1,1,2,"Business",117,0.3,"21-40",39,8,15,388.57,162,"F",100,200,9,792,140,"F",792,"F",28.09,"A"]
["Invoice number",12.56,"Machine1",299.8,1573,"John",1595928,36,16379.5,4,56.3,120,30,"A",152.6,120,60198,"2005-03-01",6,100,20,5.62,10.18,1,16,204,"G1",23,2.92,1.97,64,509,2,"Good",9.5,"Yes",2,6.2,"High","Squash","Female",27,7.8,2,1,0.25,1,0.2,3,0.3,1,2,1,"Jane",2,158,"C",16,4.6900000000000004,1,1,8.6,3.96,13.3,12.8,36,51,39,45,"C",47.6,1,3,"Social Science",27,0.1,">41",44,13,16,384.25,156,"F",200,300,16,225,140,"C",225,"C",28.09,"A"]
["Bank code",12.33,"Machine1",303.10000000000002,1384,"Mary",1480556,41,19592.5,5,55.2,130,30,"A",172.5,130,61722,"2005-04-01",12,99,12,4.04,9.81,1,35,188.9,"G1",13,2.72,1.6,56,472,0,"Good",7.5,"No",2,10.199999999999999,"High","Tennis","Female",30,7.2,2,1,0.22,1,0.2,4,0.35,2,1,1,"John",2,64,"C",12,4.66,1,1,6.34,3.73,12.4,13.4,42,44,60,39,"A",37.799999999999997,1,4,null,null,null,null,null,null,null,419.99,141,"F",300,400,26,652,140,"F",652,"F",28.09,"A"]
["Bank code",12.34,"Machine1",300.2,1521,"Mary",1370248,50,31246,1,55.3,140,40,"A",210.6,140,65888,"2005-05-01",8,105,12,4.1100000000000003,8.9499999999999993,1,45,189.6,"G1",33,2.72,1.62,56,473,1,"Good",8,"No",2,4.9000000000000004,"High","Squash","Female",29,6.6,3,1,0.23,1,0.2,5,0.4,4,-1,2,"Frances",-1,123,"C",14,4.63,1,1,6.44,3.74,7.9,8.6999999999999993,44,45,46,39,"B",38.299999999999997,1,5,null,null,null,null,null,null,null,368.61,153,"F",400,500,40,485,140,"F",485,"F",28.09,"A"]
["Address",12.73,"Machine1",299.2,1429,"John",1276418,14,10863,2,57.1,150,40,"A",228.1,150,68176,"2005-06-01",7,111,23,6.78,10.4,1,25,203.6,"G2",9,2.95,2.2200000000000002,69,534,4,"No Good",8,"Yes",2,7.1,"High","Squash","Male",30,5.4,3,1,0.27,1,0.2,6,0.45,6,-1,2,"Mary",-1,156,"C",16,4.62,1,1,10.26,4.13,10.199999999999999,10.9,45,56,50,38,"B",54.8,2,1,null,null,null,null,null,null,null,386.51,202,"C",500,600,71,674,140,"F",674,"F",28.09,"A"]
["Bank code",11.84,"Machine1",301.10000000000002,1452,"Steven",1334527,18,14212,4,52.9,160,20,"B",235.4,160,69490,"2005-07-01",9,106,12,0.59,9.7799999999999994,1,30,150.5,"G2",28,1.79,0.79,49,436,1,"Good",5.5,"Yes",3,4.2,"High","Tennis","Male",27,10.199999999999999,4,1,0.2,1,0.2,7,0.5,9,-2,2,"Jane",-1,64,"C",12,4.5999999999999996,1,1,1.41,3.24,7.6,8.4,48,38,56,51,"C",16.399999999999999,2,2,null,null,null,null,null,null,null,388.02,136,"F",600,700,133,420,140,"F",420,"F",28.09,"A"]
["Address",12.71,"Machine1",299.10000000000002,970,"John",1609988,36,31314,4,57,170,20,"B",234.1,170,67713,"2005-08-01",8,118,18,6.69,9.48,1,70,202.8,"G2",15,2.94,2.2000000000000002,69,532,4,"Good",6,"No",3,4.9000000000000004,"Low","Golf","Female",28,9.6,4,1,0.27,1,0.2,8,0.55000000000000004,13,-1,2,"John",-1,123,"C",14,4.63,1,1,10.130000000000001,4.1100000000000003,13.7,14.1,58,56,39,41,"C",54.2,2,3,null,null,null,null,null,null,null,416.63,157,"F",700,800,182,203,140,"F",203,"F",28.09,"A"]
["Address",12.77,"Machine1",304.7,1102,"Peter",1363052,81,36252.5,3,57.3,180,30,"B",268.60000000000002,180,66004,"2005-09-01",11,111,43,7.08,9.4700000000000006,1,55,206.1,"G2",22,2.61,2.2799999999999998,70,539,3,"Good",8.5,"No",2,6.4,"High","Tennis","Female",28,12,5,1,0.28000000000000003,1,0.2,9,0.6,20,1,3,"Frances",0,157,"C",16,4.5599999999999996,1,1,10.68,4.17,6.2,5.9,60,57,52,36,"B",56.6,2,4,null,null,null,null,null,null,null,366.06,177,"F",800,"*",41,608,140,"F",608,"F",28.09,"A"]
["Invoice number",12.67,"Machine1",298.7,1098,"John",1616318,63,24862.5,5,56.8,190,30,"B",253.4,190,56250,"2005-10-01",8,117,24,6.36,9.26,1,50,199.9,"G2",30,3.36,2.13,67,525,0,"Good",8,"Yes",2,7,"Low","Squash","Male",28,12,5,1,0.23,1,0.2,10,0.65,20,0,3,"Mary",0,62,"B",12,4.7,1,1,9.65,4.07,10.1,11.7,62,55,49,45,"A",52.2,2,5,null,null,null,null,null,null,null,386.85,202,"C",null,null,null,350,140,"C",350,"C",28.09,"A"]
["Bank code",11.99,"Machine1",303.39999999999998,974,"Steven",1735790,72,28483.5,7,53.6,200,40,"B",266.5,200,54061,"2005-11-01",6,104,14,1.65,13.89,2,60,215.1,"G3",18,1.96,1.03,50,440,5,"No Good",9,"Yes",2,6.6,"High","Tennis","Male",30,7.2,6,1,0.37,2,0.3,null,null,null,0,3,"Jane",0,121,"B",14,4.6500000000000004,1,1,2.92,3.39,null,null,64,39,45,51,"C",23,3,1,null,null,null,null,null,null,null,386.85,158,"F",null,null,null,360,140,"C",360,"C",28.09,"B"]
["Bank code",12.43,"Machine1",300.60000000000002,1024,"Mary",1495223,54,35538.5,5,55.7,210,40,"B",235.6,210,53025,"2005-12-01",4,87,16,4.74,12.06,2,55,156.1,"G3",7,2.79,1.77,59,487,2,"Good",7,"No",1,6.4,"High","Squash","Female",28,8.4,6,1,0.3,2,0.3,null,null,null,0,3,"John",0,151,"B",16,4.62,1,1,7.35,3.83,null,null,65,47,52,36,"A",42.2,3,2,null,null,null,null,null,null,null,416.43,148,"F",null,null,null,338,140,"F",338,"F",28.09,"B"]
["Date of application",12.83,"Machine1",300.60000000000002,1156,"Peter",2080392,86,33320,8,57.5,220,20,"C",212.1,220,54421,"2006-01-01",5,91,22,7.49,12.6,2,65,214.2,"G3",6,2.68,2.36,71,545,2,"Good",6,"No",3,6.4,"Low","Golf","Female",30,12,7,1,0.34,2,0.3,null,null,null,-2,4,"Frances",-2,60,"B",12,4.59,1,2,11.28,null,null,null,67,58,53,44,"C",59.2,3,3,null,null,null,null,null,null,null,371.45,162,"F",null,null,null,334,140,"F",334,"F",28.09,"B"]
["Address",12.74,"Machine1",299,1592,"Peter",1628507,41,28177.5,6,57.1,230,20,"C",198.5,230,54911,"2006-02-01",8,70,25,6.9,10.55,2,21,217.9,"G3",19,2.86,2.2400000000000002,69,536,5,"Good",8,"No",1,7,"Low","Squash","Male",27,12,7,1,0.38,2,0.3,null,null,null,-2,4,"Mary",-2,117,"B",14,4.62,1,2,10.42,null,null,null,69,56,null,39,"A",55.5,3,4,null,null,null,null,null,null,null,387.42,194,"C",null,null,null,463,140,"F",463,"F",28.09,"B"]
["Bank code",12.4,"Machine1",298.60000000000002,1523,"Mary",1809806,77,24344,8,55.5,240,30,"C",180.2,240,68696,"2006-03-01",3,71,14,4.5199999999999996,7.43,2,45,211,"G3",20,2.2599999999999998,1.71,58,482,0,"Good",5.5,"No",3,6.4,"Low","Golf","Female",30,10.199999999999999,8,1,0.37,2,0.3,null,null,null,-2,4,"Jane",-2,149,"B",16,4.58,1,2,7.03,null,null,null,71,46,null,40,"A",40.799999999999997,3,5,null,null,null,null,null,null,null,382.7,176,"C",null,null,null,422,140,"F",422,"F",28.09,"B"]
["Account number",13.03,"Machine1",300.10000000000002,1393,"Jane",1414878,27,29129.5,3,58.5,250,30,"C",92.6,250,71081,"2006-04-01",6,50,27,8.93,11.97,2,65,225.4,"G1",20,3.47,2.64,74,558,3,"Good",7,"No",2,5.5,"Low","Tennis","Male",27,9.6,8,1,0.33,2,0.3,null,null,null,-2,4,"John",-2,65,"B",12,4.67,1,2,13.32,null,null,null,72,null,null,44,"C",null,null,null,null,null,null,null,null,null,null,417.91,152,"F",null,null,null,393,140,"F",393,"F",28.09,"B"]
["Date of application",12.84,"Machine1",300.39999999999998,1712,"Peter",2033691,59,23485.5,8,57.6,102,40,"C",null,null,71373,"2006-05-01",4,53,19,7.58,10.45,2,65,220.8,"G1",16,2.79,2.38,72,546,0,"Good",8,"No",3,6.9,"High","Golf","Male",30,11.4,9,1,0.39,2,0.3,null,null,null,0,5,"Frances",0,113,"B",14,4.7,1,2,11.4,null,null,null,72,null,null,39,"B",null,null,null,null,null,null,null,null,null,null,367.34,151,"F",null,null,null,437,140,"F",437,"F",28.09,"B"]
["Bank code",12.02,"Machine1",300.2,1700,"Steven",1717512,63,32019.5,5,53.8,155,40,"C",null,null,64366,"2006-06-01",5,79,21,1.87,6.07,2,45,222,"G1",35,2.11,1.08,50,442,7,"Good",6,"No",2,6.4,"High","Tennis","Female",27,11.8,9,1,0.38,2,0.3,null,null,null,0,5,"Mary",0,147,"B",16,4.6500000000000004,1,2,3.24,null,null,null,72,null,null,50,"C",null,null,null,null,null,null,null,null,null,null,383.14,127,"F",null,null,null,99,140,"F",99,"F",28.09,"B"]
["Account number",12.99,"Machine1",300.5,1747,"Jane",2029361,90,41769,8,58.3,null,null,null,null,null,71956,"2006-07-01",3,76,26,8.65,9.49,2,55,214.5,"G1",43,3.55,2.59,74,556,0,"No Good",7,"No",2,6,"High","Tennis","Male",29,12.4,10,1,0.3,2,0.3,null,null,null,0,5,"Jane",0,62,"A",12,4.58,1,2,12.92,null,null,null,75,null,null,38,"B",null,null,null,null,null,null,null,null,null,null,386.55,138,"F",null,null,null,496,140,"F",496,"F",28.09,"B"]
["Bank code",12.4,"Machine1",298.7,1661,"Mary",1665359,54,38598.5,4,55.5,null,null,null,null,null,57924,"2006-08-01",12,63,14,4.47,11.8,2,70,214.8,"G1",38,2.2799999999999998,1.7,58,481,3,"Good",7.5,"No",2,7.1,"Low","Squash","Male",29,11.6,10,1,0.39,2,0.3,null,null,null,-1,5,"John",0,118,"A",14,4.6500000000000004,1,2,6.96,null,null,null,78,null,null,45,"A",null,null,null,null,null,null,null,null,null,null,414.87,133,"F",null,null,null,489,140,"F",489,"F",28.09,"B"]
["Invoice number",12.52,"Machine1",301.3,null,"Mary",1726289,50,21148,7,56.1,null,null,null,null,null,62149,"2006-09-01",3,75,null,5.33,10.81,3,30,199.7,"G2",20,2.92,1.9,62,502,3,"Good",6,"No",1,6.8,"High","Squash","Male",28,9.6,1,2,0.43,3,0.4,null,null,null,1,6,"Frances",1,99,"A",16,4.71,1,2,8.19,null,null,null,78,null,null,49,"C",null,null,null,null,null,null,null,null,null,null,371.03,170,"F",null,null,null,1943,120,"C",1943,"C",29.52,"A"]
["Address",12.72,"Machine1",301,null,"John",1512757,23,13761.5,6,57,null,null,null,null,null,59915,"2006-10-01",8,87,null,6.73,11.76,3,80,191.5,"G2",40,2.64,2.21,69,533,1,"Good",6.5,"No",2,5.8,"Low","Golf","Female",30,9,1,2,0.45,3,0.4,null,null,null,1,6,"Mary",1,65,"A",12,4.68,1,2,10.19,null,null,null,79,null,null,39,"B",null,null,null,null,null,null,null,null,null,null,390.33,163,"F",null,null,null,2497,120,"F",2497,"F",29.52,"A"]
["Bank code",12.02,"Machine1",301.39999999999998,null,"Steven",1131037,5,15062,1,53.7,null,null,null,null,null,54597,"2006-11-01",2,53,null,1.82,11.19,3,21,193.6,"G2",31,2.73,1.07,50,441,3,"Good",9,"No",2,5.7,"Low","Golf","Female",29,6.6,2,2,0.47,3,0.4,null,null,null,1,6,"Jane",1,119,"A",14,4.6100000000000003,1,2,3.16,null,null,null,80,null,null,39,"B",null,null,null,null,null,null,null,null,null,null,386.36,202,"C",null,null,null,2601,120,"F",2601,"F",29.52,"A"]
["Invoice number",12.57,"Machine1",300.2,null,"John",1482851,36,23417.5,2,56.3,null,null,null,null,null,54330,"2006-12-01",5,92,null,5.69,11.52,3,15,180,"G2",20,2.8,1.98,64,510,1,"Good",9.5,"No",2,5.5,"High","Golf","Female",28,6.5,2,2,0.4,3,0.4,null,null,null,1,6,"John",1,103,"A",16,4.66,1,2,8.6999999999999993,null,null,null,81,null,null,45,"A",null,null,null,null,null,null,null,null,null,null,421.19,161,"F",null,null,null,1663,120,"C",1663,"C",29.52,"A"]
["Bank code",12.48,"Machine1",300.2,null,"Mary",1661106,59,40009.5,6,55.9,null,null,null,null,null,null,null,4,83,null,5.04,13.18,3,125,180.7,"G2",19,3.07,1.83,61,494,0,"Good",5.5,"No",2,6.7,"High","Squash","Male",27,4.8,3,2,0.45,3,0.4,null,null,null,1,7,"Frances",2,68,"A",12,4.63,1,3,7.76,null,null,null,82,null,null,45,"A",null,null,null,null,null,null,null,null,null,null,null,147,"F",null,null,null,906,120,"F",906,"F",29.52,"A"]
["Bank code",12.34,"Machine1",300.60000000000002,null,"Mary",1595841,68,33235,7,55.3,null,null,null,null,null,null,null,6,71,null,4.09,12.13,3,110,227.5,"G3",20,2.33,1.61,56,473,1,"Good",7,"No",2,6.6,"High","Squash","Female",29,4.8,3,2,0.44,3,0.4,null,null,null,2,7,"Mary",2,120,"A",14,4.5999999999999996,1,3,6.41,null,null,null,82,null,null,36,"A",null,null,null,null,null,null,null,null,null,null,null,153,"F",null,null,null,2487,120,"F",2487,"F",29.52,"A"]
["Invoice number",12.59,"Machine1",301.3,null,"John",1582872,54,37119.5,4,56.4,null,null,null,null,null,null,null,10,94,null,5.86,12.52,3,80,198,"G3",40,3.26,2.02,65,514,1,"Good",8.5,"No",2,7.3,"High","Tennis","Male",30,9,4,2,0.42,3,0.4,null,null,null,2,7,"Jane",2,102,"A",16,4.58,1,3,8.94,null,null,null,82,null,null,39,"B",null,null,null,null,null,null,null,null,null,null,null,130,"F",null,null,null,3322,120,"F",3322,"F",29.52,"A"]
["Invoice number",12.61,"Machine1",299.2,null,"John",1643766,63,36609.5,7,56.5,null,null,null,null,null,null,null,5,95,null,6,12.51,3,99,227.1,"G3",31,2.82,2.0499999999999998,65,517,2,"Good",7,"No",3,4.8,"Low","Tennis","Male",28,8.4,4,2,0.46,3,0.4,null,null,null,1,7,"John",2,null,null,null,4.4800000000000004,1,3,9.14,null,null,null,84,null,null,39,"B",null,null,null,null,null,null,null,null,null,null,null,153,"F",null,null,null,1886,120,"F",1886,"F",29.52,"A"]
["Bank code",12.31,"Machine1",301.2,null,"Mary",1474283,41,26137.5,5,55.1,null,null,null,null,null,null,null,4,68,null,3.87,10.8,3,120,228.9,"G3",20,2.42,1.56,55,468,3,"No Good",5,"No",1,6,"Low","Tennis","Male",27,12.2,5,2,0.46,3,0.4,null,null,null,2,8,"Frances",0,null,null,null,4.57,1,3,6.1,null,null,null,84,null,null,49,"C",null,null,null,null,null,null,null,null,null,null,null,150,"F",null,null,null,2085,120,"F",2085,"F",29.52,"A"]
["Bank code",12.32,"Machine1",303.2,null,"Mary",1612783,45,27472,7,55.2,null,null,null,null,null,null,null,6,69,null,3.97,10.220000000000001,3,95,225.5,"G3",19,2.52,1.58,56,470,3,"Good",8,"No",1,7.9,"Low","Golf","Female",29,11.8,5,2,0.42,3,0.4,null,null,null,0,8,"Mary",0,null,null,null,4.5999999999999996,1,3,6.25,null,null,null,85,null,null,40,"A",null,null,null,null,null,null,null,null,null,null,null,182,"C",null,null,null,1538,120,"F",1538,"F",29.52,"A"]
["Date of application",12.79,"Machine1",300.89999999999998,null,"Peter",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,7.2,12.52,4,null,null,null,29,2.86,2.2999999999999998,null,null,0,"Good",7.5,"No",2,5.0999999999999996,"High",null,null,null,6.6,6,2,0.52,4,0.5,null,null,null,0,8,"Jane",0,null,null,null,4.6500000000000004,1,3,10.86,null,null,null,95,null,null,41,"C",null,null,null,null,null,null,null,null,null,null,null,149,"F",null,null,null,1395,120,"F",1395,"F",29.52,"B"]
["Date of application",12.78,"Machine1",298.7,null,"Peter",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,7.16,11.62,4,null,null,null,21,2.92,2.2999999999999998,null,null,0,"Good",6,"No",2,6.4,"Low",null,null,null,6,6,2,0.57999999999999996,4,0.5,null,null,null,0,8,"John",0,null,null,null,4.71,1,3,10.8,null,null,null,88,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,169,"F",null,null,null,1595,120,"F",1595,"F",29.52,"B"]
["Invoice number",12.57,"Machine1",302.89999999999998,null,"John",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,5.67,10.19,4,null,null,null,27,2.79,1.98,null,null,3,"No Good",6,"No",2,7.9,"Low",null,null,null,12,7,2,0.57999999999999996,4,0.5,null,null,null,0,9,"Frances",-1,null,null,null,4.63,1,3,8.68,null,null,null,89,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,169,"F",null,null,null,1607,120,"F",1607,"F",29.52,"B"]
["Name",13.16,"Machine1",299.2,null,"Jane",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,9.82,11.26,4,null,null,null,26,3.25,2.8,null,null,5,"Good",7.5,"Yes",2,7.4,"Low",null,null,null,11.4,7,2,0.55000000000000004,4,0.5,null,null,null,-1,9,"Mary",-1,null,null,null,4.6399999999999997,1,3,14.6,null,null,null,89,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,128,"F",null,null,null,1857,120,"F",1857,"F",29.52,"B"]
["Mobile number",12.9,"Machine1",302.2,null,"Jane",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,8.0299999999999994,9.0399999999999991,4,null,null,null,4,3.04,2.4700000000000002,null,null,4,"Good",8,"No",1,5.8,"Low",null,null,null,9.6,8,2,0.59,4,0.5,null,null,null,-1,9,"Jane",-1,null,null,null,4.68,1,3,12.04,null,null,null,90,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,161,"F",null,null,null,950,120,"C",950,"C",29.52,"B"]
["Bank code",12.28,"Machine1",300.8,null,"Steven",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,3.63,12.63,4,null,null,null,8,2.89,1.5,null,null,10,"No Good",7.5,"Yes",2,5.8,"High",null,null,null,9,8,2,0.59,4,0.5,null,null,null,-2,9,"John",-1,null,null,null,4.59,1,3,5.75,null,null,null,90,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,151,"F",null,null,null,1107,120,"F",1107,"F",29.52,"B"]
["Invoice number",12.65,"Machine1",302.60000000000002,null,"John",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,6.27,8.4600000000000009,4,null,null,null,7,3.19,2.11,null,null,0,"Good",7.5,"No",3,5.5,"Low",null,null,null,11.4,9,2,0.52,4,0.5,null,null,null,-1,10,"Frances",1,null,null,null,4.53,1,4,9.5299999999999994,null,null,null,91,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,178,"C",null,null,null,2868,120,"F",2868,"F",29.52,"B"]
["Signature",13.12,"Machine1",302,null,"Jane",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,9.51,10.96,4,null,null,null,3,2.74,2.75,null,null,3,"No Good",6.5,"No",3,4.5999999999999996,"High",null,null,null,10.8,9,2,0.56000000000000005,4,0.5,null,null,null,1,10,"Mary",1,null,null,null,4.5199999999999996,1,4,14.16,null,null,null,95,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,160,"F",null,null,null,2171,120,"F",2171,"F",29.52,"B"]
["Bank code",12.29,"Machine1",301.7,null,"Steven",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,3.74,7.64,4,null,null,null,14,2.4900000000000002,1.53,null,null,1,"Good",6.5,"No",2,7.7,"High",null,null,null,12,10,2,0.59,4,0.5,null,null,null,1,10,"Jane",1,null,null,null,4.59,1,4,5.92,null,null,null,95,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,154,"F",null,null,null,1994,120,"F",1994,"F",29.52,"B"]
["Invoice number",12.53,"Machine1",300.3,null,"John",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,5.38,9.94,4,null,null,null,19,2.37,1.91,null,null,3,"Good",8,"No",3,4.7,"High",null,null,null,12.2,10,2,0.52,4,0.5,null,null,null,1,10,"John",1,null,null,null,4.6500000000000004,1,4,8.26,null,null,null,99,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,198,"C",null,null,null,1494,120,"F",1494,"F",29.52,"B"]
["Bank code",12.13,"Machine1",301.3,null,"Steven",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,7.82,9.75,5,null,null,null,8,2.2000000000000002,1.25,null,null,1,"Good",5.5,"Yes",2,6.4,"High",null,null,null,9.6,1,3,0.65,5,0.6,null,null,null,null,null,null,null,null,null,null,4.63,1,4,4.26,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,136,"F",null,null,null,7538,100,"F",7538,"F",31.1,"A"]
["Invoice number",13.47,"Machine1",300.89999999999998,null,"Jane",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,9.5,10.32,5,null,null,null,9,3.17,3.17,null,null,1,"Good",9.5,"Yes",3,6.8,"Low",null,null,null,9.6,1,3,0.61,5,0.6,null,null,null,null,null,null,null,null,null,null,4.59,1,4,17.739999999999998,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,182,"C",null,null,null,9260,100,"F",9260,"F",31.1,"A"]
["Invoice number",12.64,"Machine1",298.10000000000002,null,"John",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,6.16,8.4600000000000009,5,null,null,null,8,2.66,2.08,null,null,2,"Good",9.5,"No",2,6,"High",null,null,null,6,2,3,0.69,5,0.6,null,null,null,null,null,null,null,null,null,null,4.6900000000000004,1,4,9.3699999999999992,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,192,"C",null,null,null,3626,100,"F",3626,"F",31.1,"A"]
["Bank code",11.85,"Machine1",301.8,null,"Steven",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,12.3,9.35,5,null,null,null,19,1.9,0.81,null,null,4,"Good",6,"No",3,4,"Low",null,null,null,6.6,2,3,0.66,5,0.6,null,null,null,null,null,null,null,null,null,null,4.6500000000000004,1,4,1.54,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,143,"F",null,null,null,3225,100,"F",3225,"F",31.1,"A"]
["Invoice number",12.56,"Machine1",304.2,null,"John",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,7.5,9.3800000000000008,5,null,null,null,18,3.02,1.96,null,null,0,"No Good",6,"Yes",1,6.1,"Low",null,null,null,5.4,3,3,0.6,5,0.6,null,null,null,null,null,null,null,null,null,null,4.63,1,4,8.57,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,167,"F",null,null,null,4308,100,"C",4308,"C",31.1,"A"]
["Bank code",12.12,"Machine1",299.10000000000002,null,"Steven",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,11.2,9.2899999999999991,5,null,null,null,20,2.57,1.23,null,null,0,"No Good",7,"No",2,4.5,"High",null,null,null,6,3,3,0.65,5,0.6,null,null,null,null,null,null,null,null,null,null,4.58,1,4,4.16,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,182,"C",null,null,null,7200,100,"F",7200,"F",31.1,"A"]
["Bank code",12.12,"Machine1",302.2,null,"Steven",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,8.6,11.06,5,null,null,null,8,2.4300000000000002,1.24,null,null,1,"Good",6,"No",2,6.5,"Low",null,null,null,9.6,4,3,0.61,5,0.6,null,null,null,null,null,null,null,null,null,null,4.63,1,4,4.21,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,207,"C",null,null,null,4479,100,"F",4479,"F",31.1,"A"]
["Address",12.75,"Machine1",300.60000000000002,null,"Peter",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,6.96,8.44,5,null,null,null,12,2.66,2.25,null,null,1,"No Good",7.5,"No",1,7.2,"High",null,null,null,9.6,4,3,0.61,5,0.6,null,null,null,null,null,null,null,null,null,null,4.62,1,4,10.51,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,187,"C",null,null,null,2016,100,"F",2016,"F",31.1,"A"]
["Bank code",12.33,"Machine1",299.60000000000002,null,"Mary",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,4,11.71,5,null,null,null,4,2.5299999999999998,1.59,null,null,4,"Good",7.5,"Yes",2,5.3,"High",null,null,null,12.6,5,3,0.67,5,0.6,null,null,null,null,null,null,null,null,null,null,4.72,2,1,6.29,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,155,"F",null,null,null,4866,100,"F",4866,"F",31.1,"A"]
["Bank code",11.99,"Machine1",299.60000000000002,null,"Steven",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,1.65,8.4700000000000006,5,null,null,null,6,2.67,1.03,null,null,2,"Good",8,"No",2,7.1,"High",null,null,null,12,5,3,0.62,5,0.6,null,null,null,null,null,null,null,null,null,null,4.6500000000000004,2,1,2.93,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,125,"F",null,null,null,2863,100,"F",2863,"F",31.1,"A"]
["Bank code",12.34,"Machine2",303,null,"Mary",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,4.07,8.61,6,null,null,null,null,2.42,1.61,null,null,2,"Good",7.5,"No",2,7.4,"Low",null,null,null,6.3,6,3,null,null,null,null,null,null,null,null,null,null,null,null,null,4.6900000000000004,2,1,6.39,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,6643,100,"F",6643,"F",31.1,"B"]
["Bank code",12.41,"Machine2",301.60000000000002,null,"Mary",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,4.57,7.91,6,null,null,null,null,2.57,1.73,null,null,5,"Good",7.5,"No",2,7.1,"Low",null,null,null,6.5,6,3,null,null,null,null,null,null,null,null,null,null,null,null,null,4.6500000000000004,2,1,7.1,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,6316,100,"F",6316,"F",31.1,"B"]
["Bank code",12.34,"Machine2",300.10000000000002,null,"Mary",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,4.0999999999999996,13.7,6,null,null,null,null,2.8,1.62,null,null,4,"Good",6.5,"No",1,5.6,"High",null,null,null,12.6,7,3,null,null,null,null,null,null,null,null,null,null,null,null,null,4.7,2,1,6.44,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,4870,100,"F",4870,"F",31.1,"B"]
["Account number",12.99,"Machine2",300.2,null,"Jane",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,8.6300000000000008,8.5299999999999994,6,null,null,null,null,3.14,2.59,null,null,7,"Good",8.5,"No",2,5,"High",null,null,null,12.6,7,3,null,null,null,null,null,null,null,null,null,null,null,null,null,4.6900000000000004,2,1,12.89,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,3010,100,"F",3010,"F",31.1,"B"]
["Signature",13.12,"Machine2",303,null,"Jane",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,9.51,8.75,6,null,null,null,null,2.99,2.75,null,null,4,"Good",6.5,"No",1,7.6,"High",null,null,null,9.6,8,3,null,null,null,null,null,null,null,null,null,null,null,null,null,4.67,2,1,14.15,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,3976,100,"F",3976,"F",31.1,"B"]
["Bank code",12.43,"Machine2",299.8,null,"Mary",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,4.68,9.06,6,null,null,null,null,2.34,1.75,null,null,1,"No Good",7.5,"Yes",1,7,"Low",null,null,null,9.6,8,3,null,null,null,null,null,null,null,null,null,null,null,null,null,4.6500000000000004,2,1,7.25,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,5662,100,"F",5662,"F",31.1,"B"]
["Bank code",12.32,"Machine2",299.10000000000002,null,"Mary",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,3.97,10.27,6,null,null,null,null,3.02,1.58,null,null,3,"Good",9.5,"Yes",2,5,"High",null,null,null,11.4,9,3,null,null,null,null,null,null,null,null,null,null,null,null,null,4.7,2,1,6.24,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,4655,100,"F",4655,"F",31.1,"B"]
["Bank code",12.2,"Machine2",300.10000000000002,null,"Steven",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,3.12,12.03,6,null,null,null,null,2.71,1.38,null,null,3,"Good",7.5,"Yes",2,9.4,"Low",null,null,null,11.4,9,3,null,null,null,null,null,null,null,null,null,null,null,null,null,4.6500000000000004,2,1,5.0199999999999996,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,3292,100,"C",3292,"C",31.1,"B"]
["Bank code",12.21,"Machine2",300.60000000000002,null,"Steven",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,3.14,9.08,6,null,null,null,null,2.17,1.38,null,null,2,"Good",6.5,"Yes",2,8,"High",null,null,null,12,10,3,null,null,null,null,null,null,null,null,null,null,null,null,null,4.58,2,1,5.05,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,2846,100,"F",2846,"F",31.1,"B"]
["Invoice number",12.61,"Machine2",302.3,null,"John",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,5.99,12.97,6,null,null,null,null,2.99,2.0499999999999998,null,null,2,"No Good",7,"No",2,6.1,"Low",null,null,null,12.6,10,3,null,null,null,null,null,null,null,null,null,null,null,null,null,4.67,2,1,9.1300000000000008,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,3956,100,"F",3956,"F",31.1,"B"]
["Bank code",12.43,"Machine2",299,null,"Mary",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,4.72,9.64,7,null,null,null,null,2.44,1.76,null,null,3,"Good",6.5,"Yes",2,5.8,"High",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,4.5999999999999996,2,2,7.32,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,19910,80,"C",19910,"C",32.86,"A"]
["Bank code",12.43,"Machine2",300.8,null,"Mary",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,4.74,11.68,7,null,null,null,null,2.68,1.76,null,null,2,"Good",6,"No",2,7.5,"High",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,4.63,2,2,7.34,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,12018,80,"F",12018,"F",32.86,"A"]
["Invoice number",12.67,"Machine2",302.39999999999998,null,"John",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,6.38,8,7,null,null,null,null,3.12,2.13,null,null,3,"No Good",6,"No",2,4.4000000000000004,"Low",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,4.63,2,2,9.68,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,16012,80,"F",16012,"F",32.86,"A"]
["Bank code",12.36,"Machine2",301.5,null,"Mary",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,4.25,11.24,7,null,null,null,null,2.8,1.65,null,null,1,"No Good",6.5,"Yes",2,6.9,"Low",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,4.5999999999999996,2,2,6.65,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,6670,80,"C",6670,"C",32.86,"A"]
["Invoice number",12.6,"Machine2",301.8,null,"John",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,5.91,9.8800000000000008,7,null,null,null,null,2.68,2.0299999999999998,null,null,5,"No Good",7.5,"Yes",2,6.2,"High",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,4.63,2,2,9.02,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,16727,80,"F",16727,"F",32.86,"A"]
["Bank code",12.26,"Machine2",301.5,null,"Steven",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,3.49,9.7799999999999994,7,null,null,null,null,2.1,1.47,null,null,3,"Good",7,"No",2,8.9,"High",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,4.58,2,2,5.56,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,12433,80,"F",12433,"F",32.86,"A"]
["Bank code",12.23,"Machine2",302.39999999999998,null,"Steven",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,3.33,3.57,7,null,null,null,null,2.38,1.43,null,null,1,"Good",8.5,"Yes",2,7.3,"Low",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,4.5999999999999996,2,2,5.32,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,7912,80,"F",7912,"F",32.86,"A"]
["Invoice number",12.56,"Machine2",300.10000000000002,null,"John",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,5.64,9.23,7,null,null,null,null,3.13,1.97,null,null,4,"No Good",6.5,"Yes",2,6.7,"Low",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,4.6500000000000004,2,2,8.6300000000000008,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,19911,80,"C",19911,"C",32.86,"A"]
["Bank code",12.08,"Machine2",297.89999999999998,null,"Steven",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,2.2599999999999998,6.39,7,null,null,null,null,2.35,1.17,null,null,2,"Good",8,"Yes",2,5.3,"Low",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,4.63,2,2,3.8,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,12288,80,"F",12288,"F",32.86,"A"]
["Bank code",12.47,"Machine2",298.8,null,"Mary",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,4.9800000000000004,8.4,7,null,null,null,null,2.74,1.82,null,null,3,"Good",9,"No",2,6.4,"High",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,4.7,2,2,7.68,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,13166,80,"F",13166,"F",32.86,"A"]
["Mobile number",12.89,"Machine2",299.5,null,"Jane",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,7.96,10.76,8,null,null,null,null,2.72,2.46,null,null,1,"No Good",7,"Yes",1,8.3000000000000007,"High",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,4.6500000000000004,2,2,11.94,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,19070,80,"F",19070,"F",32.86,"B"]
["Bank code",12.31,"Machine2",300.2,null,"Mary",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,3.86,11.5,8,null,null,null,null,2.9,1.56,null,null,1,"Good",9,"Yes",1,7.1,"High",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,4.71,2,2,6.08,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,10994,80,"F",10994,"F",32.86,"B"]
["Address",12.74,"Machine2",298.89999999999998,null,"Peter",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,6.86,12.03,8,null,null,null,null,2.5099999999999998,2.23,null,null,3,"Good",9,"Yes",1,6.6,"Low",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,4.7300000000000004,2,3,10.37,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,16203,80,"F",16203,"F",32.86,"B"]
["Bank code",12.41,"Machine2",300.89999999999998,null,"Mary",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,4.55,12.07,8,null,null,null,null,3.09,1.72,null,null,6,"Good",8,"No",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,4.6900000000000004,2,3,7.07,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,10701,80,"F",10701,"F",32.86,"B"]
["Bank code",12.33,"Machine2",299.5,null,"Mary",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,4.04,11.12,8,null,null,null,null,2.27,1.6,null,null,4,"Good",8,"Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,4.6500000000000004,2,3,6.34,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,19912,80,"C",19912,"C",32.86,"B"]
["Mobile number",12.92,"Machine2",301.3,null,"Jane",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,8.14,10.130000000000001,8,null,null,null,null,2.82,2.4900000000000002,null,null,0,"Good",8,"No",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,4.7,2,3,12.2,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,14809,80,"F",14809,"F",32.86,"B"]
["Invoice number",12.6,"Machine2",301.7,null,"John",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,5.91,10.85,8,null,null,null,null,3.32,2.0299999999999998,null,null,6,"No Good",7.5,"No",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,4.71,2,3,9.01,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,19911,80,"C",19911,"C",32.86,"B"]
["Invoice number",12.6,"Machine2",301.2,null,"John",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,5.88,11.09,8,null,null,null,null,3.13,2.02,null,null,1,"Good",11,"No",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,4.7300000000000004,2,3,8.98,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,17099,80,"F",17099,"F",32.86,"B"]
["Bank code",12.45,"Machine2",301.5,null,"Mary",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,4.82,12.01,8,null,null,null,null,2.34,1.78,null,null,1,"Good",6.5,"No",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,4.6500000000000004,2,3,7.46,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,10131,80,"C",10131,"C",32.86,"B"]
["Bank code",12.11,"Machine2",301.2,null,"Steven",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,2.48,10.99,8,null,null,null,null,2.38,1.23,null,null,0,"Good",5.5,"No",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,4.6399999999999997,2,3,4.12,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,16169,80,"F",16169,"F",32.86,"B"]
["Invoice number",12.55,"Machine2",302.39999999999998,null,"John",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,5.52,10.119999999999999,9,null,null,null,null,3.04,null,null,null,0,"Good",5,"No",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,4.6900000000000004,2,3,8.4600000000000009]
["Invoice number",12.65,"Machine2",300.10000000000002,null,"John",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,6.27,12.11,9,null,null,null,null,2.66,null,null,null,4,"Good",7.5,"No",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,4.67,2,3,9.5299999999999994]
["Mobile number",12.91,"Machine2",299.7,null,"Jane",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,8.06,13.39,9,null,null,null,null,2.86,null,null,null,1,"No Good",7,"Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,4.6399999999999997,2,3,12.09]
["Date of application",12.79,"Machine2",301.2,null,"Peter",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,7.24,13.21,9,null,null,null,null,2.68,null,null,null,1,"Good",7,"No",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,4.7300000000000004,2,3,10.92]
["Bank code",11.9,"Machine2",302.10000000000002,null,"Steven",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,1,12.47,9,null,null,null,null,2.38,null,null,null,3,"Good",6.5,"No",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,4.6500000000000004,2,4,1.99]
["Invoice number",12.53,"Machine2",299.2,null,"John",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,5.43,13.69,9,null,null,null,null,2.61,null,null,null,5,"No Good",6,"No",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,4.63,2,4,8.33]
["Mobile number",12.91,"Machine2",298.5,null,"Jane",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,8.1,12.16,9,null,null,null,null,3.46,null,null,null,2,"No Good",7.5,"No",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,4.6399999999999997,2,4,12.14]
["Bank code",12.45,"Machine2",300.89999999999998,null,"Mary",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,4.83,10.63,9,null,null,null,null,2.97,null,null,null,2,"Good",8,"Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,4.6399999999999997,2,4,7.47]
["Invoice number",12.64,"Machine2",303.60000000000002,null,"John",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,6.17,10.43,9,null,null,null,null,3.21,null,null,null,3,"Good",6.5,"No",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,4.59,2,4,9.39]
["Bank code",12.5,"Machine2",300.39999999999998,null,"Mary",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,5.21,12.43,9,null,null,null,null,3,null,null,null,2,"Good",7.5,"No",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,4.5999999999999996,2,4,8.02]
["Bank code",12.51,"Machine2",299.60000000000002,null,"Mary",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,5.27,12.84,10,null,null,null,null,2.59,null,null,null,1,"Good",8.5,"Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,4.63,2,4,8.1]
["Bank code",12.47,"Machine2",299.39999999999998,null,"Mary",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,5,10.86,10,null,null,null,null,2.9,null,null,null,2,"No Good",8,"No",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,4.63,2,4,7.72]
["Bank code",12.39,"Machine2",297.8,null,"Mary",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,4.41,11.64,10,null,null,null,null,2.2599999999999998,null,null,null,2,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,4.5999999999999996,2,4,6.87]
["Bank code",12.43,"Machine2",302.39999999999998,null,"Mary",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,4.6900000000000004,12.85,10,null,null,null,null,2.48,null,null,null,0,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,4.6900000000000004,2,4,7.28]
["Bank code",12.32,"Machine2",301.10000000000002,null,"Mary",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,3.91,11.29,10,null,null,null,null,2.46,null,null,null,4,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,4.58,2,4,6.16]
["Bank code",12.02,"Machine2",300.5,null,"Steven",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,1.85,10.56,10,null,null,null,null,2.29,null,null,null,3,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,4.5999999999999996,2,4,3.22]
["Bank code",12.29,"Machine2",299.10000000000002,null,"Steven",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,3.74,11.67,10,null,null,null,null,2.98,null,null,null,2,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,4.63,3,1,5.92]
["Signature",13.11,"Machine2",300.5,null,"Jane",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,9.4700000000000006,9.3699999999999992,10,null,null,null,null,3.19,null,null,null,1,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,4.58,3,1,14.11]
["Bank code",12.04,"Machine2",301.8,null,"Steven",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,1.95,10.59,10,null,null,null,null,2.39,null,null,null,0,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,4.57,3,1,3.36]
["Bank code",12.42,"Machine2",302.60000000000002,null,"Mary",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,4.62,11.56,10,null,null,null,null,2.48,null,null,null,1,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,4.6500000000000004,3,1,7.16]
[null,12.4,"Machine3",301.3,null,"Mary",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,4.4800000000000004,null,null,null,null,null,null,2.4700000000000002,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,4.59,3,1,6.81]
[null,12.49,"Machine3",301.10000000000002,null,"Mary",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,5.15,null,null,null,null,null,null,3.07,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,4.62,3,1,6.13]
[null,12.2,"Machine3",299.5,null,"Steven",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,3.07,null,null,null,null,null,null,2.33,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,4.57,3,1,6.3]
[null,12.48,"Machine3",301.60000000000002,null,"Mary",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,5.07,null,null,null,null,null,null,2.64,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,4.6100000000000003,3,1,5.17]
[null,12.3,"Machine3",303,null,"Mary",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,3.83,null,null,null,null,null,null,2.38,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,4.5599999999999996,3,1,5.22]
[null,12.6,"Machine3",299.10000000000002,null,"John",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,5.89,null,null,null,null,null,null,2.38,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,4.6500000000000004,3,1,7.13]
[null,12.53,"Machine3",301.5,null,"John",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,5.42,null,null,null,null,null,null,2.33,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,4.63,3,1,2.7]
[null,12.2,"Machine3",299.89999999999998,null,"Steven",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,3.08,null,null,null,null,null,null,2.75,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,4.6100000000000003,3,1,7.06]
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[null,11.99,"Machine4",null,null,"Steven",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,2.0499999999999998,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,4.6399999999999997,4,2,4.66]
[null,12.49,"Machine4",null,null,"Mary",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,3.11,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,4.67,4,2,6.32]
[null,12.25,"Machine4",null,null,"Steven",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,2.0699999999999998,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,4.58,4,3,3.9]
[null,12.83,"Machine4",null,null,"Peter",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,3.24,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,4.6900000000000004,4,3,5.84]
[null,12.57,"Machine4",null,null,"John",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,2.64,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,4.6900000000000004,4,3,7.97]
[null,12.71,"Machine4",null,null,"John",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,2.87,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,4.63,4,3,5.04]
[null,12.94,"Machine4",null,null,"Jane",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,3.42,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,4.58,4,3,7.18]
[null,12.37,"Machine4",null,null,"Mary",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,2.3199999999999998,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,4.63,4,3,5.54]
[null,12.53,"Machine4",null,null,"John",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,2.33,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,4.57,4,3,5.17]
[null,12.08,"Machine4",null,null,"Steven",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,2.0099999999999998,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,4.6500000000000004,4,3,8.1]
[null,12.6,"Machine4",null,null,"John",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,2.4,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,4.7,4,3,6.5]
[null,12.43,"Machine4",null,null,"Mary",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,2.85,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,4.7300000000000004,4,3,6.49]
[null,13.03,"Machine4",null,null,"Jane",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,2.68,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,4.67,4,3,5.73]
[null,12.14,"Machine4",null,null,"Steven",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,2.5299999999999998,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,4.62,4,3,4.0599999999999996]
[null,12.93,"Machine4",null,null,"Jane",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,2.69,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,4.57,4,4,6.23]
[null,12.59,"Machine4",null,null,"John",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,2.7,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,4.6100000000000003,4,4,6.76]
[null,12.38,"Machine4",null,null,"Mary",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,2.52,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,4.63,4,4,8.0500000000000007]
[null,12.19,"Machine4",null,null,"Steven",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,1.99,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,4.6500000000000004,4,4,7.46]
[null,12.48,"Machine4",null,null,"Mary",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,2.48,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,4.6100000000000003,4,4,3]
[null,12.27,"Machine4",null,null,"Steven",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,2.4,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,4.59,4,4,6.16]
[null,13.25,"Machine4",null,null,"Jane",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,3.7,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,4.58,4,4,8.07]
[null,12.16,"Machine4",null,null,"Steven",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,2.2599999999999998,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,4.5599999999999996,4,4,5.74]
[null,11.93,"Machine4",null,null,"Steven",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,2.34,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,4.62,4,4,6.69]
[null,12.38,"Machine4",null,null,"Mary",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,2.2400000000000002,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,4.71,4,4,6.01]
[null,12.54,"Machine4",null,null,"John",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,2.72,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,4.6500000000000004,4,4,6.05]
[null,12.93,"Machine4",null,null,"Jane",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,3.59,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,4.6399999999999997,4,4,5.86]
[null,12.53,"Machine4",null,null,"John",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,2.64,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,5.44]
[null,12.43,"Machine4",null,null,"Mary",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,2.93,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,5.64]
[null,12.81,"Machine4",null,null,"Peter",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,2.59,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,5.08]
[null,12.78,"Machine4",null,null,"Peter",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,2.54,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,3.61]
[null,12.63,"Machine4",null,null,"John",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,2.61,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,4.96]
[null,12.68,"Machine4",null,null,"John",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,3.08,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,9.0500000000000007]
[null,13.32,"Machine4",null,null,"Jane",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,3.59,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,3.68]
[null,12.38,"Machine4",null,null,"Mary",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,2.86,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,5.58]

{"sheet":"ProcessMAHelp","index":1,"n_rows":446,"n_cols":3,"rows_kept":446,"cut":false,"hidden":false,"merged":[]}
["Tools","Section","Details"]
["STATISTICS"]
["BASIC STATISTICS"]
["Descriptive Statistics","Title","Displays descriptive statistics for a given set of data"]
[null,"Details","• Mean - represents the center of the data and is equals to sum of all observations divided by the number of observations\n• Std Dev - Standard deviation measures the degree of dispersion of the data from the mean. The greater the value, the greater the spread\n• Variance - equals to the square of standard deviation\n• Count - number of observations\n• Sum - sum of all observations\n• Min - smallest value of the data\n• 1st quartile - 25% of the data are less than or equal to this value \n• Median - 50% of the data are less than or equal to this value \n• 3rd quartile - 75% of the data are less than or equal to this value \n• Max - largest value of the data \n• Range - different between the largest and smallest value of the data \n• Mean 95% CI-L and Mean 95% CI-U - lower and upper confidence interval limits for the mean \n• Sigma 95% CI-L and Mean 95% CI-U - lower and upper confidence interval limits for the standard deviation \n• Median 95% CI-L and Mean 95% CI-U - lower and upper confidence interval limits for the median\n "]
[null,"How to","• Choose ProcessMA > Statistics > Descriptive Statistics\n• In Variable, select the column containing the data\n• Click OK"]
[null,"Example","You collected data on time (in minutes) to resolve a customer enquiry in a call centre. You want to describe this set of data.\n• Open data worksheet by choosing ProcessMA > Tools > Data \n• Choose ProcessMA > Statistics > Descriptive Statistics\n• In Variable, select BJ - Time \n• Click OK "]
[null,"Results","The call center takes a average of 7.0430 minutes to resolve a customer enquiry."]
["1-Sample Z","Title","The 1-Sample Z conducts a hypothesis test of the mean based on sampled data when the population standard deviation, σ is known. "]
[null,"Details","It also calculates a confidence interval of the mean. This procedure is based on normal distribution. For larger samples (>30), the sample standard deviation may be used in the absence of the population standard deviation. For smaller samples, make sure the data is drawn from a normal distribution or the t-test may be more appropriate.\n\nTest                   Null Hypothesis, H0              Alternate Hypothesis, H1  \nOne-tailed        μ = μ0                                     μ < μ0 or μ > μ0 \nTwo-tailed        μ = μ0                                     μ <> μ0 \n\nwhere μ is the population mean and μ0 is the hypothesised population mean"]
[null,"How to","• Choose ProcessMA > Statistics > Basic Statistics > 1-Sample Z\n• In Variable, select the column containing the data (Numeric)\n• In Test Mean, enter hypothesized population mean (Numeric)\n• In Sigma, enter population standard deviation (Numeric, >0)\n• In Alternate, select the appropriate alternate test\n• In Confidence Level, enter value for confidence level (Numeric, >0 & <1)\n• Click OK "]
[null,"Example","You measured the thickness of 30 new widgets made. You know that the thicknesses of these parts are normally distributed with a standard deviation of 1.4. You want to test if the population mean is 57 and also calculate a 90% confidence interval for the mean.\n• Open data worksheet by choosing ProcessMA > Tools > Data\n• Choose ProcessMA > Statistics > Basic Statistics > 1-Sample Z\n• In Variable, select K - Thickness\n• In Test Mean, enter 57 \n• In Sigma, 1.4 \n• In Confidence Level, enter 0.90 \n• Click OK "]
[null,"Results","For a desired α = 0.05, since p = 0.0002 < α, we will reject H0. Therefore, we conclude that there is significant evidence that the population mean is not equal to 57. Therefore, H0 will also be rejected for α = 0.10."]
["1-Sample t","Title","The 1-Sample t conducts a hypothesis test of the mean based on sampled data when the population standard deviation, σ is unknown."]
[null,"Details","It also calculates a confidence interval of the mean. This procedure is based on the t-distribution which is derived from a normal distribution. It is more conservative than the Z-test for smaller sample sizes or when s is unknown.\n\nTest                   Null Hypothesis, H0              Alternate Hypothesis, H1  \nOne-tailed        μ = μ0                                     μ < μ0 or μ > μ0 \nTwo-tailed        μ = μ0                                     μ <> μ0 \n\nwhere μ is the population mean and μ0 is the hypothesised population mean"]
[null,"How to","• Choose ProcessMA > Statistics > Basic Statistics > 1-Sample t \n• In Variable, select the column containing the data (Numeric)\n• In Test Mean, enter hypothesized population mean (Numeric)\n• In Alternate, select the appropriate alternate test\n• In Confidence Level, enter value for confidence level (Numeric, >0 & <1)\n• Click OK"]
[null,"Example","You made measurements on 12 parts. You know that the measurements are normally distributed but the population standard deviation is unknown. You want to test if the population mean is less than 4 and calculate the 95% confidence interval for the mean.\n• Open data worksheet by choosing ProcessMA > Tools > Data\n• Choose ProcessMA > Statistics > Basic Statistics > 1-Sample t \n• In Variable, select BK - Measurement \n• In Test Mean, enter 4 \n• In Alternate, select Less than \n• Click OK"]
[null,"Results","For a desired α = 0.05, since p = 0.0694 > a, we fail to reject H0. Therefore, we conclude that there is no significant evidence that the population mean is less than 4."]
["2-Sample t","Title","The 2-Sample t conducts a hypothesis test of the difference between two population means when the population standard deviation, σ is unknown."]
[null,"Details","It also calculates a confidence interval of the mean. This procedure is based on the t-distribution which is derived from a normal distribution. The samples should be drawn independently from each other. For dependent samples, use the Paired t-test.\n\nTest                   Null Hypothesis, H0              Alternate Hypothesis, H1  \nOne-tailed        μ1 - μ2 = d                              μ1 - μ2 = d or μ1 - μ2 > d\nTwo-tailed        μ1 - μ2 = d                              μ1 - μ2 <> d\n\nwhere μ1 and μ2 are the population means and d is the hypothesised difference between the population means."]
[null,"How to","• Choose ProcessMA > Statistics > Basic Statistics > 2-Sample t \nFor data in different columns \n• In Variable 1, select the column containing the data for the first sample (Numeric) \n• In Variable 2, select the column containing the data for the second sample (Numeric)\n\nFor data in single stacked column \n• In Variable, select the column containing the data for both samples (Numeric)\n• In Subgroup, select the column containing the subgroup indicator (Exactly 2 distinct values) \n\n• In Test Mean Difference, enter hypothesized difference between the population means (Numeric) \n• In Alternate, select the appropriate alternate test\n• In Confidence Level, enter value for confidence level (Numeric, >0 & <1)\n• Check Assume Equal Variances, if you want to assume that both populations have equal variances\n• Click OK"]
[null,"Example","A tire manufacturer wants to compare the wear and tear of 2 types of new tires, A and B. Ten motorcycles were fitted with Tire A and another ten motocycles were fitted with Tire B. After 6 months, the amount of wear and tire on the tires were measured.\n• Open data worksheet by choosing ProcessMA > Tools > Data\n• Choose ProcessMA > Statistics > Basic Statistics > 2-Sample t \n• In Variable 1, select BL - Tire-A \n• In Variable 2, select BM - Tire-B\n• Click OK"]
[null,"Results","For a desired α = 0.05, since p = 0.6491 > α, we fail to reject H0. Therefore, we conclude that there is no significant evidence that the wear and tear of the two types of new tires are different."]
["Paired t","Title","The Paired t conducts a hypothesis test of the difference between two population means when observations are paired."]
[null,"Details","It also calculates a confidence interval of the difference. This procedure is based on the t-distribution which is derived from a normal distribution. It is appropriate when the paired differences follow a normal distribution. If the observations are dependent in a pairwise manner, the matching results in smaller variance and greater power of detecting differences than the 2-sample t.\n\nTest                   Null Hypothesis, H0              Alternate Hypothesis, H1  \nOne-tailed        μd = μD                                  μd < μD or μd > μD\nTwo-tailed        μd = μD                                  μd <> μD\n\nwhere μd is the population mean of the differences and μD is the hypothesized mean of the differences"]
[null,"How to","• Choose ProcessMA > Statistics > Basic Statistics > Paired-t \n• In Variable 1, select the column containing the data for the first sample (Numeric) \n• In Variable 2, select the column containing the data for the second sample (Numeric, same number of data points as Variable 1)\n• In Test Mean Difference, enter hypothesized difference between the population means (Numeric)\n• In Alternate, select the appropriate alternate test\n• In Confidence Level, enter value for confidence level (Numeric, >0 & <1)\n• Click OK"]
[null,"Example","A tire manufacturer wants to compare 2 types of tires, A and B. Ten motorcycles were fitted with each type of tires in random (either front or back). After 6 months, the amount of wear and tire on the tires were measured. You want to use a Paired t procedure as it removes the variation due to difference between motorcycles.\n• Open data worksheet by choosing ProcessMA > Tools > Data\n• Choose ProcessMA > Statistics > Basic Statistics > Paired-t\n• In Variable 1, select BL - Tire-A \n• In Variable 2, select BM - Tire-B\n• Click OK"]
[null,"Results","For a desired α = 0.05, since p = 0.025 < α, we will reject H0. Therefore, we conclude that there is significant evidence that the two types of tires wear out differently."]
["1 Proportion","Title","The 1 Proportion conducts a hypothesis test and calculates a confidence interval of the population proportion."]
[null,"Details","It is a test of one binomial proportion.\n\nTest                         Null Hypothesis, H0                  Alternate Hypothesis, H1  \nOne-tailed              p = p0                                         p < p0 or p > p0 \nTwo-tailed              p = p0                                         p <> p0 \n\nwhere p is the population proportion and p0 is the hypothesised value"]
[null,"How to","• Choose ProcessMA > Statistics > Basic Statistics > 1 Proportion \n\nFor Summarized Data: \n• In No. of Trials, enter the number of trials (Integer, >=Successes) \n• In No. of Successes, enter the number of successes within the set of trials (Integer, >=0) \n\nFor Raw Data: \n• In Variable, select the column containing the raw data (Exactly 2 distinct values, success and failure)\n• In Test Proportion, enter hypothesized proportion (Numeric, >0 & <1)\n\n• In Alternate, select the appropriate alternate test\n• In Confidence Level, enter value for confidence level (Numeric, >0 & <1)\n• Click OK"]
[null,"Example","A telecommunication company recently launched a new customer help service. The company conducted a customer survey to find out if customer satisfaction has improved from last year’s 68%. 860 customers were randomly selected for the survey and of which 590 were satisfied.\n• Open data worksheet by choosing ProcessMA > Tools > Data\n• Choose ProcessMA > Statistics > Basic Statistics > 1 Proportion \n• Click Summarized Data\n• In No. of Trials, enter 860 \n• In No. of Successes, enter 590 \n• In Test Proportion, enter 0.68 \n• In Alternate, select Greater than \n• Click OK"]
[null,"Results","For a desired α = 0.05, since p = 0.3519 > α, we fail to reject H0. Therefore, we conclude that there is no significant evidence that customer satisfaction has improved."]
["2 Proportions","Title","The 2 Proportions conducts a hypothesis test of the difference between two proportions and calculates a confidence interval."]
[null,"Details","Test                     Null Hypothesis, H0                Alternate Hypothesis, H1  \nOne-tailed          p1 - p2 = p0                             p1 - p2 < p0 or p1 - p2 > p0 \nTwo-tailed          p1 - p2 = p0                            p1 - p2 <> p0 \n\nwhere p1 and p2 are the proportions of success in populations 1 and 2 respectively, and p0 is the hypothesized difference between the two proportions."]
[null,"How to","Choose ProcessMA > Statistics > Basic Statistics > 2 Proportions\n\nFor Summarized Data: \n• In No. of Trials (1), enter the number of trials for the first sample (Integer, >=Successes) \n• In No. of Successes (1), enter the number of successes within the set of trials for the first sample (Integer, >=0) \n• In No. of Trials (2), enter the number of trials for the second sample (Integer, >=Successes) \n• In No. of Successes (2), enter the number of successes within the set of trials for the second sample (Integer, >=0) \n\nFor Raw Data: \n• In Variable 1, select the column containing the raw data for the first sample (Exactly 2 distinct values, success and failure)\n• In Variable 2 , select the column containing the raw data for the second sample (Exactly 2 distinct values, success and failure)\n\n• In Test Difference , enter hypothesized proportion (Numeric, >-1 & <1)\n• In Alternate, select the appropriate alternate test\n• In Confidence Level, enter value for confidence level (Numeric, >0 & <1)\n• Click OK"]
[null,"Example","You are the property manager and you need to decide whether to change the brand of light bulb you are using for the entire building. You want to use the brand of light bulbs that blow their fuses less often. You installed 400 light bulbs of the existing brand and 600 light bulbs of the new brand. After two months, you found out that 45 light bulbs of the existing brand 71 light bulbs of the new brand blew their fuses.\n• Open data worksheet by choosing ProcessMA > Tools > Data\n• Choose ProcessMA > Statistics > Basic Statistics > 2 Proportions\n• Click Summarized Data\n• In No. of Trials (1), enter 400\n• In No. of Successes (1), enter 45\n• In No. of Trials (2), enter 600\n• In No. of Successes (2), enter 71\n• In Alternate, select Less than \n• Click OK"]
[null,"Results","For a desired α = 0.05, since p = 0.3884 > α, we fail to reject H0. Therefore, we conclude that there is no significant evidence that the new brand of light bulbs blow their fuses less often the existing brand."]
["Chi-Square and Contingency Table","Title","The χ2 procedure tests if there is association between the classification of one variable and the classification of another variable."]
[null,"Details","The data must be summarized and presented in a table form where the cells contains frequency counts for various levels. The null hypothesis states that no association exists. ProcessMA highlights to you the number of cells with expected frequencies less than 5. This is because the chi-square test may not be reliable is more than 20% of the cells are less than 5 and especially when they have a significant contribution to chi-square statistics (small p value). An alternative method is to combine categories so that cells with small expected frequencies are treated as one.\nNote: Limited to 10 variables at one time."]
[null,"How to","Choose ProcessMA > Statistics > Basic Statistics > Chi-Square and Contingency Table\n• In Variables, select the columns containing the data (Numeric, >=2 Variables)\n• In Label, select column containing row labels for the variables\n• Click OK"]
[null,"Example","You want to find out if there is a connection between age group and flavours of biscuits they like. You surveyed 200 people and recorded the number of people that chose the different flavours they like.\n• Open data worksheet by choosing ProcessMA > Tools > Data\n• Choose ProcessMA > Statistics > Basic Statistics > Chi-Square and Contingency Table\n• In Variables, select BZ - Chocolate, CA - Strawberry, CB - Vanilla \n• In Label, select BY - Age \n• Click OK"]
[null,"Results","For a desired α = 0.05, since p = 0. 438 > α, we fail to reject H0. Therefore, we conclude that there is no significant evidence that age and their liking for different flavours of biscuits are related."]
["Chi-Square Goodness-of-Fit Test","Title","Chi-Square Goodness of Fit (GOF) tests if the data follows a multi-nominal distribution with certain proportions."]
[null,"Details","If the proportions are not specified, the categories are assumed to have equal proportions. You can also specify assumed proportions to test. ProcessMA GOF can analyze raw or summarized data. In the case of raw data, the frequency count can be left empty (assumed = 1) and specified proportions for each category must be the same. Note that the chi-square may not be reliable if the expected frequency of any category is less than 5.\n\nNull Hypothesis, H0: Data follow a multi-nomial distribution with certain proportions \nAlternate Hypothesis, H1: Data do not follow a multi-nomial distribution with certain proportions"]
[null,"How to","• Choose ProcessMA > Statistics > Basic Statistics > Chi-Square Goodness-of-Fit Test \n• In Category, select the column containing the categorical data (>= 2 distinct values) \n• In Frequency, select the column containing frequency counts (Positive integer) \n• In Proportions, select the column containing block levels (Optional, Numeric, >0 & <1) \n• Click OK"]
[null,"Example","You want to assess if the new student’s interests in the different faculties are similar to the previous year. You have collected data on 300 new student’s interest.\n• Open data worksheet by choosing ProcessMA > Tools > Data\n• In Category, select BV - Interest \n• In Frequency, select BW - Count \n• In Proportions, select BX - Probability\n• Click OK"]
[null,"Results","For a desired α = 0.05, since p = 0.003 < α, we can reject H0 and conclude that the interest in different faculties for the new students is different from the previous year."]
["Correlation","Title","Correlation calculates the Pearson product moment correlation coefficients for each pair of variables and it is used to test if variables are correlated."]
[null,"Details","The correlation coefficient measures the magnitude of the linear relationship between two variables and it ranges from -1 and +1. If two variables are perfectly correlated such that when one variable increases, the other increases as well, the correlation coefficient is +1. On the other hand, if one variable increase while the other decreases, the correlation coefficient is negative. \n\nNote: Limited to 10 variables at one time."]
[null,"How to","• Choose ProcessMA > Statistics > Basic Statistics > Correlation \n• In Variables, select the columns containing the data (Numeric, >=2 Variables) \n• Click OK"]
[null,"Example","You have data on the sales revenue, number of sales representatives on the field, the amount spent on marketing and the range of products offered. You want to find out if there are correlated.\n• Open data worksheet by choosing ProcessMA > Tools > Data\n• Choose ProcessMA > Statistics > Basic Statistics > Correlation\n• In Variables, select G - Sales, H - Reps, I - Marketing, J - Products \n• Check Plot Partial\n• Click OK"]
[null,"Results","Except between Marketing and Products, low p-values suggest that correlations among variables are not zero."]
["Covariance","Title","This tool calculates the covariance for each pair of variables and can be used to measure the relationship between two variables"]
[null,"Details","Unlike Pearson correlation coefficient, covariance value is not standardized using standard deviation of the pair of variables. \nNote: Limited to 10 variables at one time."]
[null,"How to","• Choose ProcessMA > Statistics > Basic Statistics > Covariance \n• In Variables, select the columns containing the data (Numeric, >=2 Variables) \n• Click OK"]
[null,"Example","You have data on the sales revenue, number of sales representatives on the field, the amount spent on marketing and the range of products offered. You want to find out if there are correlated.\n• Open data worksheet by choosing ProcessMA > Tools > Data\n• Choose ProcessMA > Statistics > Basic Statistics > Covariance\n• In Variables, select G - Sales, H - Reps, I - Marketing, J - Products \n• Check Plot Partial\n• Click OK"]
["Power and Sample Size","Title","This procedure can calculate power, sample size and minimum difference."]
[null,"Details","For the 1-Sample Z test, 1-Sample t, 2-Sample t, 1 Proportion, 2 Proportions, One-Way ANOVA. It also includes a simple sample size calculator for both continuous and discrete data. "]
[null,"How to","• Choose ProcessMA > Statistics > Power and Sample Size \nFor sample size, difference and power value, provide values in any 2 to calculate the other"]
[null,"Example","For 1-Sample Z, 1-Sample t, 2-Sample t, One-Way ANOVA and Simple Sample Size Calculator for continuous data:\n• You are the quality assurance manager for a printer cartridge plant. You need to ensure that printer cartridges are filled with a 60ml of ink and cannot vary more than ±2ml. You know from past records that the standard deviation is 3ml. Determine how many samples you need to take at a confidence level of 99% (a = 0.01) and power values of 0.8 and 0.9?\n\nFor 1 Proportion, 2 Proportions and Simple Sample Size Calculator for discrete data:\n• You are the logistic manager and you need to find out if the proportion of products damaged during transport changed after using a new packaging. Historically the proportion of goods damaged during transport is 0.1. Determine the number of samples you need to detect a difference of 0.05 at a confidence level of 95% (a = 0.05) for a power of 0.9?\n\n• Choose ProcessMA > Tools > Load Examples\n• In Category, select Statistics \n• In Tool, select Power and Sample Size"]
["Normality Test","Title","This tool generates a normal probability plot and conducts a hypothesis test to determine is the data is normally distributed."]
[null,"Details","The chart is similar to data plotted onto a normal probability paper with a fitted cumulative distribution function (with parameters estimated based on the data). \n\nNull Hypothesis, H0: Data follow a normal distribution\nAlternate Hypothesis, H1: Data do not follow a normal distribution"]
[null,"How to","• Choose ProcessMA > Statistics > Normality Test \n• In Variable, select the column containing the data (Numeric) \n• Click OK"]
[null,"Example","You measured the thickness of 30 new widgets made. You want to find out if the data is normally distributed before performing a hypothesis test.\n• Open data worksheet by choosing ProcessMA > Tools > Data\n• Choose ProcessMA > Statistics > Normality Test \n• In Variable, select K - Thickness \n• Click OK"]
[null,"Results","The normal probability plot shows that most data follows the fitted line. The p-value is 0.3602 indicates that there is evidence that the data follow a normal distribution."]
["Generate Random Data","Title","This procedure generates random data"]
[null,"Details","• Chi-square distribution - used when outcomes are positive and such that X follows a normal distribution (where square of X then follows a chi-square)\n• Normal distribution - used when data follows a bell curve \n• F distribution - commonly used in test of variance \n• t distribution - similar to normal distribution with its tail spreading out wider \n• Uniform distribution - used to model data within a range of values and have an equal probabilities of occurrence\n• Bernoulli distribution - distibution with binary outcomes \n• Binomial distribution - based on probability of success given a specific number of trials \n• Hypergeometric distribution - used for permanent samples taken from small populations\n• Discrete distribution - user specified distribution using different values and its expected probabilities of occurrence\n• Integer distribution - user specified distribution with a range of integer values and each have an equal probabilities of occurrence\n• Poisson distribution - used when the probability of occurence is small \n• Beta distribution - used to model distribution of order statistics \n• Exponential distribution - used to time based data where failure rate is constant \n• Gamma distribution - used to model data that are positive and skewed \n• Lognormal distribution - commonly used to model reliability data and such that X follows a normal distribution (where LogX then follows Lognormal) \n• Triangular distribution - used when data is within a range and peaks at a value in between \n• Weibull distribution - commonly used to model failure times"]
[null,"How to","• Choose ProcessMA > Statistics > Generate Random Data \n• In Distribution, select the type of distribution you want to generate data from.\n• In No. of data points, enter the number of data points you want to generate per column.\n• In Output data in, select an existing available column to display the random data. \n\nFor Chi-square distribution\n• In Degrees of freedom, enter the number of degrees of freedom to define the Chi-square Distribution (Integer) \nFor Normal distribution\n• In Mean, enter the value to use as the center of the normal distribution (Numeric) \n• In Standard deviation, enter the value to use as the standard deviation of the Normal Distribution (Numeric, >0) \nFor F distribution\n• In Numerator DoF, enter the number of degrees of freedom for the effect (Positive integer) \n• In Denominator DoF, enter the number of degrees of freedom for the error (Positive integer)\nFor t distribution\n• In Degrees of freedom, enter the number of degrees of freedom to define the t Distribution (Positive integer)\nFor Uniform distribution\n• In Lower end-point, enter the value to define the minimum value for the Uniform Distribution (Numeric) \n• In Upper end-point, enter the value to define the maximum value for the Uniform Distribution (Numeric) \nFor Bernoulli distribution\n• In Probability of success, enter a value for the probability of success (between 0 and 1) to define the Bernoulli Distribution (Numeric, between 0 and 1) \nFor Binomial distribution\n• In Number of trials, enter the number of trials to define the Binomial Distribution (Positive integer) \n• In Probability of success, enter a value for probability of success (between 0 and 1) to define the Binomial Distribution (Numeric, between 0 and 1)\nFor Hypergeometric distribution\n• In population size, enter the population size (Positive integer) \n• In No. of successes in population, number of successes in the population. (Positive integer between 0 and the population size)\n• In Sample size, enter the sample size. (Positive integer between 0 and the population size)"]
[null,"How to","For Discrete distribution\n• In Values, select the column containing the values you want to be included in the distribution\n• In Probability of values, select the column containing the probabilities that correspond to the discrete numbers in the Values\nFor Integer distribution\n• In Minimum value, enter the starting value (Integer)\n• In Maximum value, enter the ending value (Integer) For Poisson distribution\n• In Mean, enter the mean value to define the Poisson Distribution. (Numeric, between 0 and 709)\nFor Beta distribution\n• In First shape parameter, enter a value for the first shape parameter to define the Beta Distribution (Numeric, >0) \n• In Second shape parameter, enter a value for the second shape parameter to define the Beta Distribution (Numeric, >0)\nFor Exponential distribution\n• In Mean, enter the mean value to define the Exponential Distribution (Numeric) \nFor Gamma distribution\n• In First shape parameter, enter a value for the first shape parameter to define the Gamma Distribution (Numeric, >0)\n• In Second shape parameter, enter a value for the second shape parameter to define the Gamma Distribution (Numeric, >0)\nFor Lognormal distribution\n• In Location, enter a value for the location to define the Lognormal Distribution (Numeric)\n• In Scale, enter a value for the scale to define the Lognormal Distribution (Numeric, >0)\nFor Triangular distribution\n• In Lower end-point, enter the value to define the minimum value for the Triangular Distribution (Numeric)\n• In Mode, enter the value to define the mode for the Triangular Distribution (Numeric)\n• In Upper end-point, enter the value to define the maximum value for the Triangular Distribution (Numeric)\nFor Weibull distribution\n• In First shape parameter, enter a value for the first shape parameter to define the Weibull Distribution (Numeric, >0)\n• In Second shape parameter, enter a value for the second shape parameter to define the Weibull Distribution (Numeric, >0)"]
[null,"Example","You want to generate 30 data data points from the Normal distribution with a mean of 10 and a standard deviation of 2.5. You want to store the data in Column A \n• Choose ProcessMA > Statistics > Generate Random Data\n• Complete the dialog box as shown in the figure below and click OK \n• The data will be stored in Column A of the current worksheet "]
["Sample Data Column","Title","This tool helps you randomly select specified number of data points from a data column. The output will be display in a new column in the same worksheet."]
[null,"How to","Choose ProcessMA > Statistics> Sample Data Column \n• In Variable, select the column to sample from\n• In No. of data points per sample, enter the number of data points for each sample\n• In No. of samples, enter the number of samples to display\n• Click OK"]
["ANOVA"]
["One-Way ANOVA","Title","The One-Way Analysis of Variance (ANOVA) is like an extension of the two-sample t-test."]
[null,"Details","It is use to compare the equality of more than two means. The residuals and fitted values of the response are shown in Columns AA:AB.\n\nNull Hypothesis, H0: μ1 = μ2 = ... = μi\nAlternate Hypothesis, H1: μ1 <> μ2 <> ... <> μi \nwhere μi are the means of population i"]
[null,"How to","• Choose ProcessMA > Statistics > ANOVA > One-Way ANOVA \n\nFor data in single stacked column \n• In Variable, select the column containing the response data (Numeric) \n• In Factor, select the column containing factor levels (>=2 levels) \n\nFor data in different columns \n• In Variables, select the columns containing the response data (Numeric, >= 2 variables)\n\n• In Confidence Level, enter the desired confidence level for the confidence interval (Numeric, >0 & <1) \n• Check Show Boxplot, if you want to display boxplot of the data \n• Check Plot Residual, if you want to display residual plots\n• Click OK"]
[null,"Example","A company makes steel bolts using four different machines. You want to assess if the dimensions of the steel bolts made are the same for the different machines. You randomly selected 50 steel bolts made by each machine.\n• Open data worksheet by choosing ProcessMA > Tools > Data\n• Choose ProcessMA > Statistics > ANOVA > One-Way ANOVA\n• In Variable, select B - Dimension \n• In Factor, select C - Machine\n• Check Show Boxplot\n• Click OK"]
[null,"Results","For a desired α = 0.05, since p = 0.3068> α, we fail to reject H0. Therefore, we conclude that there is no significant evidence that the dimensions of the steel bolts made by the different machines are different. It can also be observed from the individual confidence intervals that there are significant overlaps. The residual plots should also be examined to ensure that the residuals are normally distributed, centered about zero and random."]
["Two-Way ANOVA","Title","The Two-Way Analysis of Variance tests the equality of means of populations classified by two factors."]
[null,"Details","It requires the data to be balanced (all factor combinations must have the same number of observations). The residuals and fitted values of the response are shown in Columns AA:AB."]
[null,"How to","• Choose ProcessMA > Statistics > ANOVA > Two-Way ANOVA \n• In Variable, select the column containing the response data (Numeric) \n• In Factor 1, select the column containing first factor levels (>=2 levels) \n• In Factor 2 , select the column containing second factor levels (>=2 levels) \n• Check Additive Model, if you want to fit the model without the interaction term\n• In Confidence Level, enter the desired confidence level for the confidence interval (Numeric, >0 & <1) \n• Check Show Boxplot, if you want to display boxplot of the data \n• Check Plot Residual, if you want to display residual plots\n• Click OK"]
[null,"Example","You conducted an experiment to study how well organisms multiple in different temperatures and in the presence of different catalysts. You prepared 18 dishes of organisms and placed them at three different temperatures and added three different types of catalyst. You recorded the number of organism in each dish after 10 days. You want to use the Two-Way ANOVA to test if there is significant evidence of main and interactions effects.\n• Open data worksheet by choosing ProcessMA > Tools > Data\n• Choose ProcessMA > Statistics > ANOVA > Two-Way ANOVA\n• In Variable, select L - Organism \n• In Factor 1 , select M - Temperature \n• In Factor 2 , select N - Catalyst\n• Click OK"]
[null,"Results","For a desired α = 0.05, there is no significant evidence for the temperature and temperature*catalyst interaction effects. There is significant evidence for the catalyst main effects on the growth of the organisms since p = 0.002 < α. From the confidence interval, it suggests that catalyst B promotes the growth of the organism more than the other two."]
["Fully Nested ANOVA","Title","This tool performs a fully nested analysis of variance and estimates the variance components for the response variable."]
[null,"Details","For unbalanced design, F values and P values will not be calculated. The design must be hierarchically nested with fixed factors. To use this tool, response variables and factors must be presented in columns. Factors must have at least 2 distinct levels and need not be balanced to analysis. The residuals and fitted values of the response are shown in Columns AA:AB.\n\nNote: Limited to 10 variables at one time."]
[null,"How to","• Choose ProcessMA > Statistics > ANOVA > Fully Nested ANOVA\n• In Response, select the column containing the response data\n• In Term 1 to Term 10 , select the column containing data for the respective model terms (>= 2 distinct values) \n• Check Plot Residuals, to display residual plots\n• Click OK"]
[null,"Example","You want to identify the sources of variability in the making of concrete. You conduct an experiment and measure strength of the concrete for four mixes over four different batches. You take three measurements at each batch. You want to use Fully Nested ANOVA to analyze your data.\n• Open data worksheet by choosing ProcessMA > Tools > Data\n• Choose ProcessMA > Statistics > ANOVA > Fully Nested ANOVA\n• In Response, select BG - Strength \n• In Term 1, select BH - Mix \n• In Term 2, select BI - Batch\n• Click OK"]
[null,"Results","The ANOVA table indicates that there is significant evidence for mix and batch main effects at α = 0.05, since p < 0.05. The variance component estimates indicate that the variability attributable to mix and batch are 17.6% and 8.3% of the total variability respectively."]
["General Linear Model","Title","General Linear Model (GLM) is used to perform univariate analysis of variance with balanced and unbalanced designs and regression for the response variable."]
[null,"Details","It is commonly used to analyze data of experimental designs. The residuals and fitted values of the response are shown in Columns AA:AB. Response variables and terms must be presented in columns. Covariates must be numeric and factors must have at least 2 distinct levels. The Model can include factors, covariates, interactions and nested term. Multiple terms must be separated by commas. Use * to represent interactions and () to represent nesting. The model must be hierachical, if an interaction term is included, all lower order interactions and main terms must also be included."]
[null,"How to","• Choose ProcessMA > Statistics > ANOVA > General Linear Model\n• In Response, select the column containing the response data\n• In Term 1 to Term 10 , select the column containing data for the respective model terms and choose if the term is a covariate or a factor (Covariate: Numeric)\n• In Model, enter the terms to be included in the model. Multiple terms must be separated by commas. Use * to represent interactions and () to represent nesting. Model must be hierachical\n• Check Plot Residuals, to display residual plots\n• Click OK"]
[null,"Example","You conducted an experiment to study the effect of material type and blade size on the wind generated by an electric fan. There are 3 types of materials and 3 blade sizes. The material type is a fixed factor and the blade size is a covariate.\n• Open data worksheet by choosing ProcessMA > Tools > Data\n• Choose ProcessMA > Statistics > ANOVA > General Linear Model\n• In Response, select BD - Wind \n• In Term 1, select BE - Material and choose Factor\n• In Term 2, select BF - BladeSize and choose Covariate\n• In Model, enter Material, BladeSize, Material*BladeSize \n• Click OK"]
[null,"Results","From the ANOVA table, all the p-values are less than 0.005 which indicate that there are significant evidences on the effects. The R-sq shows that the model explains 89.7% of the variance in wind."]
["Analysis of Means","Title","Analysis of Means (ANOM) is used to test the equality of population means and it's function is similar to ANOVA."]
[null,"Details","An ANOM chart looks like a control chart and is used to detect population means that are different from others. You can assume if the response data follows a Normal, Binomial distribution or Poisson distribution. For Normal distribution, you can also choose between the one-way or two-way design.\n• For Normal data, one-way designs can be balanced or unbalanced and two-way designs must be balanced.\n• For Binomial data, the sample size must be sufficiently large to ensure a valid Normal approximately to Binomial since decision limits are based on Normal distribution. Therefore, a general rule to use ANOM for Binomial data is where np > 5 and n(1-p) > 5, where n is the sample size and p is the proportion of defectives\n• For Poisson data, the sample size must be constant. The Poisson mean must also be sufficiently large to ensure a valid Normal approximately to Poisson since decision limits are based on Normal distribution. Therefore, a general rule to use ANOM for Poisson data, the mean of the Poisson distribution is >=5."]
[null,"How to","• Choose ProcessMA > Statistics > ANOVA > Analysis of Means\n\nFor Normal (1 Factor): \n• In Variable, select the column containing the response data (Numeric) \n• In Factor 1, select the column containing factor levels (>=2 levels)\n\nFor Normal (2 Factors): \n• In Variable, select the column containing the response data (Numeric) \n• In Factor 1, select the column containing first factor levels. Two-way designs must be balanced (>=2 levels) \n• In Factor 2 , select the column containing second factor levels (>=2 levels)\n\nFor Binomial: \n• In Variable, select the column containing the response data (Integer, >=0, Up to 500 rows) \n• In Sample Size, enter the sample size (Positive integer) \n\nFor Poisson: \n• In Variable, select the column containing the response data (Integer, >=0, Up to 500 rows)\n• In Alpha Level, enter a value for the error rate (Numeric, >0 & <1) \n• Click OK "]
[null,"Example","You conducted an experiment to study how well organisms multiple in different temperatures (Factor 1) and in the presence of different catalysts (Factor 2). You prepared 18 dishes of organisms and placed them at three different temperatures and added three different types of catalyst. You recorded the number of organism in each dish after 10 days.\n• Open data worksheet by choosing ProcessMA > Tools > Data\n• Choose ProcessMA > Statistics > ANOVA > Analysis of Means\n\nFor Normal (1 Factor): \n• In Variable, select L - Organism\n• In Factor 1, select M - Temperature\n\nFor Normal (2 Factors): \n• In Variable, select L - Organism\n• In Factor 1, select M - Temperature\n• In Factor 2 , select N - Catalyst\n\nFor Binomial: \n• In Variable, select L - Organism\n• In Sample Size, enter 1000 \n\nFor Poisson: \n• In Variable, select L - Organism\n• Click OK"]
[null,"Results","For normal data with one factor (temperature): The main effects are within the decision limits, indicating no significant evidence of main effects.\n\nFor normal data with 2 factors: The interactions effects are within the decision limits, indicating no significant evidence of interaction. For the main effects, The main effects for level 2 and 3 of Factor 2 (Catalyst) are outside the decision limits, indicating that these means are different from the grand mean.\n\nFor Binomial data: The samples that falls outside the decision limits indicate that the sample is different from the grand mean. \n\nFor Poisson data: The samples that falls outside the decision limits indicate that the sample is different from the grand mean."]
["Test of Equal Variances","Title","The Test of Equal Variances conducts hypothesis tests for the equality variances using F, Bartlett's and Levene's tests."]
[null,"Details","The F Test is performed in place of the Bartlett's test when there are only two levels. Many statistical procedures like ANOVA and 2-Sample t-test assumes that samples are taken from populations with equal variances. This procedure can be used to valid this assumption.\n\nNull Hypothesis, H0: (σ1)^2 = (σ2)^2 = ... = (σi)^2\nAlternate Hypothesis, H1: (σ1)^2 <> (σ2)^2 <> ... <> (σi)^2 \nwhere (σi)^2 are the variances of population i"]
[null,"How to","• Choose ProcessMA > Statistics > ANOVA > Test of Equal Variances \n\nFor data in single stacked column \n• In Variable, select the column containing the response data (Numeric) \n• In Factor, select the column containing factor levels (>=2 levels) \n\nFor data in different columns \n• In Variables, select the columns containing the response data (Numeric, >= 2 variables)\n\n• In Confidence Level, enter the desired confidence level for the confidence interval (Numeric, >0 & <1) \n• Check F-Test or Barlett's, if you want to perform the f-test (factor with 2 levels) or Barlett's test \n• Check Levene's, if you want to perform the Levene's test \n• Click OK"]
[null,"Example","A company makes steel bolts using four different machines. You want to assess if the variation in dimensions of the steel bolts made are the same for the different machines. You randomly selected 50 steel bolts made by each machine.\n• Open data worksheet by choosing ProcessMA > Tools > Data\n• Choose ProcessMA > Statistics > ANOVA > Test of Equal Variances \n• In Variable, select B - Dimension \n• In Subgroup, select C - Machine\n• Check F-Test or Barlett's\n• Check Levene's\n• Click OK "]
[null,"Results","The p-value of the tests is 0.3735 and 0.401 for Barlett’s and Levene’s tests respectively. For a desired a of 0.05, since p > α, we fail to reject H0. Therefore, we conclude that there is no significant evidence that the variances are different."]
["REGRESSION"]
["Regression (Single Predictor)","Title","This procedure performs regression with a single predictor, in linear, second-order or third-order polynomial terms. "]
[null,"Details","The residuals and fitted values of the response are shown in Columns AC:AD."]
[null,"How to","• Choose ProcessMA > Statistics > Regression > Regression (Single Predictor)\n• In Response, select the column containing the response data (Numeric)\n• In Predictor, select the column containing the predictor data (Numeric)\n• In Model, choose the order of the regression equation\n• Check Plot Residual, if you want to display residual plots \n• Check Plot Fitted Line, if you want to display the fitted line plot\n• Check Show Confidence Bands, if you want to plot confidence bands in the fitted line plot\n• Check Show Prediction Bands, if you want to plot prediction bands in the fitted line plot\n• In Confidence Level, enter the desired confidence level (Numeric, >0 & <1) \n• Click OK "]
[null,"Example","You want to model the relationship between the size of the valve and the speed of the machine using a quadratic model. You collected data on various settings of the valve size and the resultant speed of the machine.\n• Open data worksheet by choosing ProcessMA > Tools > Data\n• Choose ProcessMA > Statistics > Regression > Regression (Single Predictor)\n• In Response, select O - Speed \n• In Predictor, select P - Valve \n• In Model, choose Quadratic \n• Check Plot Residual\n• Check Plot Fitted Line\n• Check Show Confidence Bands\n• Check Show Prediction Bands\n• Click OK"]
[null,"Results","The p value for the model suggests a good fit to the data. The R-sq value indicates that about 94% of the variation in speed is explained by the variation in the valve size. The 95% CL lines are the confidence limits for the machine speed and the 95% PL lines are the prediction limits for new observations."]
["Regression (Multiple Predictors)","Title","This tool performs regression to study and model the relationship between the response and one or more predictors."]
[null,"Details","ProcessMA Regression using the least squares method which minimizes the sum of squared errors to get parameter estimates. The residuals and fitted values of the response are shown in Columns AA:AB. "]
[null,"How to","• Choose ProcessMA > Statistics > Regression > Regression (Multiple Predictors) \n• In Response, select the column containing the response data (Numeric)\n• In Predictors, select the columns containing the predictors data (Numeric)\n• Check Fit Intercept, to fit a constant term (y-intercept). Otherwise the model will go through the origin\n• Check SSeq, to calculate sequential sum of squares \n• Check Show VIF, to calculate variance inflation factors, a measure of multicollinearity among predictors\n• Check Show Durbin-Watson, to calculate Durbin-Watson statistics, detects the autocorrelation in the residuals\n• Check Show Predicted SS and R-Sq, if you want to calculate the predicted sum of squares and R-Sq\n• Check Plot Residual, if you want to display residual plots \n• Click OK"]
[null,"Example","You know that sales revenue is dependent on the number of sales representative on the field, the amount spend on marketing and the range of products offered. You gathered data from 30 branches and you want to model the relationship and also predict the sales for the new branch.\n• Open data worksheet by choosing ProcessMA > Tools > Data\n• Choose ProcessMA > Statistics > Regression > Regression (Multiple Predictors) \n• In Response, select G - Sales \n• In Predictors, select H - Reps, I - Marketing, J - Products \n• Click OK"]
[null,"Results","The p values for number of representatives and product range is small, indicating that there is significant evidence that the coefficients of these predictors are not zero. The p value for amount spent on marketing is 0.874, indicating that there is no significant evidence that its coefficient is not zero. There, the amount spent on marketing will not contribute much to the prediction of sales revenue."]
["Binary Logistic Regression","Title","Logistic regression is used to study the relationship between a response variable and its predictor(s), where the response variable is categorical."]
[null,"Details","Binary Logistic Regression is used to perform logistic regression on a response variable that is binary. Examples of a binary variable is such as Yes/No, Fail/Pass, etc. This tool can also generate diagnostic plots which can be used to identify data that are not well fitted.\n\nResponse variables and terms must be presented in columns. Covariates must be numeric and factors must have at least 2 distinct levels. The Model can include factors, covariates, interactions and nested term. Multiple terms must be separated by commas. Use * to represent interactions and () to represent nesting. The model must be hierachical, if an interaction term is included, all lower order interactions and main terms must also be included.\n\nProcessMA uses maximum likelihood estimates to model parameters."]
[null,"How to","• Choose ProcessMA > Statistics > Regression > Binary Logistic Regression \n• In Response, select the column containing the response data (Exactly 2 distinct values)\n• In Term 1 to Term 10 , select the column containing data for the respective model terms and choose if the term is a covariate or a factor (Covariate: Numeric)\n• In Model, enter the terms to be included in the model. \n• In Event, choose the reference event of the response\n• In Link Function, choose the function to fit the response model\n• Check Plot Diagnostic, to display diagnostic plots of Delta chi-square, Delta deviance, Delta beta (Standardised) and Delta beta\n• Click OK"]
[null,"Example","You want to understand the effect of number of hours of sleep and smoking on blood pressure. You classified the blood pressure into Good and No Good. \n• Open data worksheet by choosing ProcessMA > Tools > Data\n• Choose ProcessMA > Statistics > Regression > Binary Logistic Regression \n• In Response, select AH - Pressure \n• In Term 1, select AI - Sleep Hours and choose Covariate \n• In Term 2, select AJ - Smoker and choose Factor \n• In Model, enter Sleep Hours, Smoker\n• In Event, choose Good \n• Click OK"]
[null,"Results","From the logistic regression table, you can obtain the coefficients for the regression model. In additions, the p values for Sleep Hours and Smoker are less than 0.05 which indicates that there is sufficient evidence that their coefficients are not zero."]
["Ordinal Logistic Regression","Title","Ordinal Logistic Regression is used to perform logistic regression on a response variable that has 3 or more levels and these levels have a natural ordering."]
[null,"Details","Examples of an ordinal variable is such as Agree/Neutral/Disagree and Small/Medium/Large/Extra Large.\n\nResponse variables and terms must be presented in columns. Covariates must be numeric and factors must have at least 2 distinct levels. The Model can include factors, covariates, interactions and nested term. Multiple terms must be separated by commas. Use * to represent interactions and () to represent nesting. The model must be hierachical, if an interaction term is included, all lower order interactions and main terms must also be included.\n\nProcessMA uses maximum likelihood estimates to model parameters."]
[null,"How to","• Choose ProcessMA > Statistics > Regression > Ordinal Logistic Regression \n• In Response, select the column containing the response data\n• In Term 1 to Term 10 , select the column containing data for the respective model terms and choose if the term is a covariate or a factor (Covariate: Numeric)\n• In Model, enter the terms to be included in the model. \n• In Link Function, choose the function to fit the response model\n• Click OK"]
[null,"Example","You want to understand the effect of amount of pesticides and humidity on the life span of mosquitoes. You have classified life span as 1 (< 2 day), 2 (2 to 4 days) and 3 (4 to 6 days).\n• Open data worksheet by choosing ProcessMA > Tools > Data\n• Choose ProcessMA > Statistics > Regression > Ordinal Logistic Regression \n• In Response, select AK - Lifespan \n• In Term 1, select AL - Pesticide and choose Covariate \n• In Term 2, select AM - Humidity and choose Factor \n• In Model, enter Pesticide, Humidity\n• Click OK"]
[null,"Results","From the logistic regression table, you can obtain the coefficients for the regression model. Constant(1) and Constant(2) are estimated intercept for lifepan 1 and 2 respectively. The p value for Humidity is 0.795 which indicates that there is insufficient evidence to conclude that humidity have an effect on mosquito population."]
["Nominal Logistic Regression","Title","Nominal Logistic Regression is used to perform logistic regression on a response variable that has 3 or more levels and these levels have no natural ordering."]
[null,"Details","Examples of an nominal variable is such as North/South/East/West and Blue/Red/Green/Yellow.\n\nResponse variables and terms must be presented in columns. Covariates must be numeric and factors must have at least 2 distinct levels. The Model can include factors, covariates, interactions and nested term. Multiple terms must be separated by commas. Use * to represent interactions and () to represent nesting. The model must be hierachical, if an interaction term is included, all lower order interactions and main terms must also be included.\n\nProcessMA uses maximum likelihood estimates to model parameters."]
[null,"How to","• Choose ProcessMA > Statistics > Regression > Nominal Logistic Regression \n• In Response, select the column containing the response data\n• In Term 1 to Term 10 , select the column containing data for the respective model terms and choose if the term is a covariate or a factor (Covariate: Numeric)\n• In Model, enter the terms to be included in the model. \n• In Event, choose the reference event of the response\n• Click OK"]
[null,"Example","You want to understand the type of sports people like to play and how is this associated with their gender and age.\n• Open data worksheet by choosing ProcessMA > Tools > Data\n• Choose ProcessMA > Statistics > Regression > Nominal Logistic Regression \n• In Response, select AN - Sports \n• In Term 1, select AO - Gender and choose Factor\n• In Term 2, select AP - Age and choose Covariate\n• In Model, enter Gender, Age \n• In Event, choose Golf\n• Click OK"]
[null,"Results","From the logistic regression table, you can obtain the coefficients for the regression model. There are two sets of parameter estimates, Squash and Tennis as compared to Golf."]
["NONPARAMETRIC"]
["1-Sample Sign","Title","The 1-Sample Sign is a nonparametric test of population location (median) and also calculates the corresponding point estimate and confidence interval."]
[null,"Details","Its parametric counterpart is the 1-sample Z and 1-sample t tests. Nonparametric tests do not make assumptions that the population is from a specific distribution. Therefore its results are more robust than a parametric test when such assumptions are violated.\n\nTest                    Null Hypothesis, H0                Alternate Hypothesis, H1  \nOne-tailed         m = m0                                     m < m0 or m > m0 \nTwo-tailed         m = m0                                     m <> m0 \n\nwhere m is the population median and m0 is the hypothesised population median"]
[null,"How to","• Choose ProcessMA > Statistics > Nonparametric > 1-Sample Sign \n• In Variable, select the column containing the data (Numeric)\n• In Test Median, enter hypothesized population median (Numeric)\n• In Alternate, select the appropriate alternate test\n• In Confidence Level, enter value for confidence level (Numeric, >0 & <1)\n• Click OK"]
[null,"Example","You are a school teacher and you want to find out if the median score for the English test has improved and you also want to obtain a 90% confidence interval for the population median. Past records show that the population median for similar English tests of the same grade was 68.\n• Open data worksheet by choosing ProcessMA > Tools > Data\n• Choose ProcessMA > Statistics > Nonparametric > 1-Sample Sign \n• In Variable, select BN - Score \n• In Test Median, enter 68 \n• In Alternate, select Greater than \n• Click OK"]
[null,"Results","For a desired α = 0.05, since p = 0.0192 < α, we will reject H0. Therefore, we conclude that there is significant evidence that the median score for the English test has improved. The 90% confidence interval of the median is (69.82, 82) and it is interpolated from the confidence levels below and above the requested level."]
["1-Sample Wilcoxon","Title","The 1-Sample Wilcoxon is a nonparametric test of the population location (median) and it also calculates the corresponding point estimate and confidence interval."]
[null,"Details","It assumes that the data are a random sample from a continuous and symmetric population. Its parametric counterpart is the 1-sample Z and 1-sample t-tests. Nonparametric tests do not make assumptions that the population is from a specific distribution. Therefore its results are more robust than a parametric test when such assumptions are violated.\n\nTest                    Null Hypothesis, H0                Alternate Hypothesis, H1  \nOne-tailed         m = m0                                     m < m0 or m > m0 \nTwo-tailed         m = m0                                     m <> m0 \n\nwhere m is the population median and m0 is the hypothesised population median"]
[null,"How to","• Choose ProcessMA > Statistics > Nonparametric > 1-Sample Wilcoxon\n• In Variable, select the column containing the data (Numeric)\n• In Test Median, enter hypothesized population median (Numeric)\n• In Alternate, select the appropriate alternate test\n• In Confidence Level, enter value for confidence level (Numeric, >0 & <1)\n• Click OK"]
[null,"Example","You are a school teacher and you want to find out if the median score for the English test has improved and also want to obtain a 90% confidence interval for the population median. Past records show that the population median for English test of the same grade was 68.\n• Open data worksheet by choosing ProcessMA > Tools > Data\n• Choose ProcessMA > Statistics > Nonparametric > 1-Sample Wilcoxon\n• In Variable, select BN - Score \n• In Test Median, enter 68 \n• In Alternate, select Greater than \n• Click OK"]
[null,"Results","For a desired a = 0.05, since p = 0.0427> a, we fail to reject H0. Therefore, we conclude that there is no significant evidence that the median score for the English test has improved. The 90% confidence interval of the median is (67, 80.5)."]
["2-Sample Mann-Whitney","Title","The 2-Sample Mann-Whitney (or two-sample Wilcoxon rank sum test) is a nonparametric test of the equality of two population medians."]
[null,"Details","It also calculates the corresponding point estimate and confidence interval. Its parametric counterpart is the Paired t test. This procedure assumes that the samples are randomly and independently drawn from two populations that have the same shape.\n\nTest                    Null Hypothesis, H0                Alternate Hypothesis, H1  \nOne-tailed         m1 = m2                                   m1 < m2 or m1 > m2 \nTwo-tailed         m1 = m2                                   m1 <> m2 \n\nwhere m1 and m2 are population medians"]
[null,"How to","• Choose ProcessMA > Statistics > Nonparametric > 2-Sample Mann-Whitney \n• In Variable 1, select the column containing the data for the first sample (Numeric) \n• In Variable 2, select the column containing the data for the second sample (Numeric)\n• In Alternate, select the appropriate alternate test\n• Click OK"]
[null,"Example","The number of printers sold by two teams of salespeople was recorded for the previous month. You want to find out if there is a difference in the population median of sales between the teams.\n• Open data worksheet by choosing ProcessMA > Tools > Data\n• Choose ProcessMA > Statistics > Nonparametric > 2-Sample Mann-Whitney\n• In Variable 1, select BO - Sales A \n• In Variable 2, select BP - Sales B \n• Click OK"]
[null,"Results","The median for both sales team A and B are 51 and 52 respectively. For a desired α = 0.05, since p = 0.7995 > α, we fail to reject H0. Therefore, we conclude that there is no significant evidence that the sales of the two teams are the different."]
["Kruskal-Wallis","Title","The Kruskal-Wallis is a nonparametric test of the equality of medians for two or more populations."]
[null,"Details","Its parametric counterpart is the One-Way Analysis of Variance. This procedure assumes that the samples are randomly and independently drawn from populations that have the same shape. It is more robust than the Mood's median test for data of many distributions but is less robust for data with outliers.\n\nNull Hypothesis, H0: m1 = m2 = ... = mi\nAlternate Hypothesis, H1: m1 <> m2 <> ... <> mi \n\nwhere mi are the medians of population i"]
[null,"How to","• Choose ProcessMA > Statistics > Nonparametric > Kruskal-Wallis\n\nFor data in single stacked column \n• In Variable, select the column containing the response data (Numeric) \n• In Factor, select the column containing factor levels (>=2 levels) \n\nFor data in different columns \n• In Variables, select the columns containing the response data (Numeric, >= 2 variables)\n\n• Click OK"]
[null,"Example","You are the manager of the mortgage department in a bank. You have three officers processing mortgage applications. You collected data on cycle time to process applications for the last 2 months and you want to assess if the three officers have the same processing speed.\n• Open data worksheet by choosing ProcessMA > Tools > Data\n• Choose ProcessMA > Statistics > Nonparametric > Kruskal-Wallis\n• In Variable, select BQ - Cycle Time \n• In Factor, select BR - Officer \n• Click OK"]
[null,"Results","For a desired α = 0.05, since p = 0.0002 < α, we will reject H0. Therefore, we conclude that there is significant evidence that the median cycle times for the three officers are different."]
["Mood's Median Test","Title","The Mood's Median Test is a nonparametric test of the equality of medians for two or more populations."]
[null,"Details","Its parametric counterpart is the One-Way Analysis of Variance. This procedure assumes that the samples are randomly and independently drawn from populations that have the same shape. It is more robust than the Kruskal-Wallis for data with outliers and is appropriate for preliminary stages of analysis.\n\nNull Hypothesis, H0: m1 = m2 = ... = mi\nAlternate Hypothesis, H1: m1 <> m2 <> ... <> mi \n\nwhere mi are the medians of population i"]
[null,"How to","• Choose ProcessMA > Statistics > Nonparametric > Mood's Median Test \n\nFor data in single stacked column \n• In Variable, select the column containing the response data (Numeric) \n• In Factor, select the column containing factor levels (>=2 levels) \n\nFor data in different columns \n• In Variables, select the columns containing the response data (Numeric, >= 2 variables)\n\n• Click OK"]
[null,"Example","You are the manager of the mortgage department in a bank. You have three officers processing mortgage applications. You collected data on cycle time to process applications for the last 2 months and you want to assess if the three officers have the same processing speed.\n• Open data worksheet by choosing ProcessMA > Tools > Data\n• Choose ProcessMA > Statistics > Nonparametric > Mood's Median Test\n• In Variable, select BQ - Cycle Time \n• In Factor, select BR - Officer \n• Click OK"]
[null,"Results","For a desired α = 0.05, since p = 0 < α, we will reject H0. Therefore, we conclude that there is significant evidence that the median cycle times for the three officers are different."]
["Friedman","Title","The Friedman test is a nonparametric analysis of a randomized block experiment."]
[null,"Details","It's parametric counterpart is the Two-Way Analysis of Variance. It requires the data to be balanced (all factor combinations must have the same number of observations) and only one observation per combination.\n\nNull Hypothesis, H0: All treatment effects = 0\nAlternate Hypothesis, H1: All treatment effects <> 0  "]
[null,"How to","• Choose ProcessMA > Statistics > Nonparametric > Friedman \n• In Variable, select the column containing the response data (Numeric, exactly 1 observation per treatment-block combination) \n• In Treatment, select the column containing treatment levels (>=2 levels) \n• In Block, select the column containing block levels (>=2 levels) \n• Click OK"]
[null,"Example","You want to conduct an experiment to assess the strength of concrete with different types of hardener. You prepared 15 blocks of concrete using three types of hardener on five different batches of cement, and tested their strengths.\n• Open data worksheet by choosing ProcessMA > Tools > Data\n• In Variable, select BS - Strength \n• In Treatment, select BT - Hardener\n• In Block, select BU - Batch \n• Click OK"]
[null,"Results","For a desired α = 0.05, since p = 0.4493 > α, we fail to reject H0. Therefore, we conclude that there is no significant evidence that the treatment effects are not zero."]
["DESIGN OF EXPERIMENT"]
["Create Factorial Design","Title","This tool generates 2-level designs full factorial for 2- 7 factors, fractional factorials for 2 - 15 factors and Plackett-Burman designs for 2 - 47 factors."]
[null,"Details","You can label your factors, specify if they are numeric or text and assign values for each factor levels. \n\n2- Level Factorial Design: You can add center points to help you detect curvatures in the fitted data. Center points are added for numeric factors and to each block. If there is a mix of numeric and text factors, pseudo center points are added. To take into consideration other incidental factors such as changes in environment conditions, you can add blocks to the design. For example, if the experiment is to be conducted over several days and the environmental conditions varies, observations obtained in the same day can be in the same block. The number of blocks available depends on the number of factors and number of replicates specified. \n\nPlackett-Burman Design: This is a type of 2-level fractional factorial designs that is commonly used to study main effects. Such designs can be used if 2-way interactions are not significant and you only wish to study main effects. A set of possible number of runs can be chosen based on the number of factors. Similarly, you can add center points and blocks. To add blocks, you need to replicate the runs and each replicate is one block.\n\nThe design matrix will be stored in a new worksheet. The cells containing the design matrix are protected to prevent unintended modifications. You can perform the experiement and enter data for each run in the columns after the design matrix for analysis later."]
[null,"How to","• Choose ProcessMA > DOE > Create Factorial Design\n• In Type of Design, choose to create a 2-level factorial design or Plackett-Burman design\n\nFor 2-level factorial fesign\n• In Number of Factors, choose the number of factors for the design\n• In Design, choose from the available designs for the number of factors chosen\n• In Number of Center Points, choose the number of centre points to be added per block of the design\n• In Number of Replicates, choose the number of replications for the corner points\n• In Number of Blocks, choose the number of blocks from the possible choices (based on design and number of replicates)\n\nFor Plackett-Burman design \n• In Number of Factors, choose the number of factors for the design\n• In Number of Runs, choose the number of runs for the design\n• In Number of Center Points, choose the number of centre points to be added per block of the design\n• In Number of Replicates, choose the number of replications for the corner points\n• Check Block Design, if you want to block the design by replicates\n• Check Randomize Runs, if you want to randomise the runs in the design\n• In Factors table, enter the Type, Name, Low levels and High levels for each factor\n• Click OK"]
[null,"Example","You want to investigate how temperature, intensity of light and type of catalyst affect the growth of organisms. Since you have sufficient resources to perform 24 runs, you want to generate a full factorial design for three factors, with three replicates.\n• Choose ProcessMA > DOE > Create Factorial Design\n• In Type of Design, choose 2-level factorial design\n• n Number of Factors, choose 3 \n• In Design, choose Full Factorial, 8 Runs, 2^3 \n• In Number of Center Points, choose 0 \n• In Number of Replicates, choose 3 \n• In Number of Blocks, choose 1 \n• In Factors table for Factor 1 \n• In Type, choose Numeric \n• In Name, enter Temp \n• In Low, enter 10 \n• In High, enter 40 \n• In Factors table for Factor 2 \n• In Type, choose Numeric \n• In Name, enter Light \n• In Low, enter 100 \n• In High, enter 300 \n• In Factors table for Factor 3 \n• In Type, choose Text \n• In Name, enter Catalyst \n• In Low, enter P\n• In High, enter Q \n• Click OK"]
[null,"Results","You collected data and enter into the Response column "]
["Analyze Factorial Design","Title","This tool analyzes the factorial design to fit a model."]
[null,"Details","ProcessMA generates a default set of terms to be included in the model but you can also add or remove these terms. If you have center points and blocks in the design, you can also choose to model center points and block effects respectively. This tool also allows you to generate effects plots and residual plots to assess model adequacy. The residuals and fitted values of the response are shown in Columns AA:AB.\n\nProcessMA will only be able to analyze designs that it creates. If you need to analyze existing design, you need to recreate the design matrix."]
[null,"How to","• Choose ProcessMA > DOE > Create Factorial Design\n• In Response, select the column containing the response data (Numeric)\n• Under Terms Tab, in Maximum Order of Terms, choose the maximum order of terms to include in the model\n• Under Terms Tab, in Available Terms, double-click on any terms to include it in the model\n• Under Terms Tab, in Selected Terms, double-click on any terms to exclude it from the model\n• Under Terms Tab, check Include Center Points, if you want to include center points in the analysis\n• Under Terms Tab, check Include Blocks, if you want to include blocking in the analysis\n• Under Results Tab, check Plot Residuals, to display the residual plot\n• Under Results Tab, check Show Pareto Plot of Effect, to display a Pareto chart of the effects\n• Under Results Tab, in Alpha, enter the level used to determine the significance of the effects (Numeric, >0 & <1) \n• Click OK"]
[null,"Example","You want to investigate how temperature, intensity of light and type of catalyst affect the growth of organisms. You created a full factorial design for three factors and with three replicates. You ran the experiments and recorded the data.\nRefer to Create Factorial Design help file to create a design for analysis \n• Choose ProcessMA > DOE > Analyze Factorial Design\n• In Response, select H - Response \n• Under Results Tab, check Show Pareto Plot of Effect\n• Click OK"]
[null,"Results","From p values in the analysis of variance table, it suggests that the main effects and the 2-way interaction are significant while the 3-way interaction is not. From the p values in the estimated effects and coefficients, it suggests that only the two main effects (Temp and Light) and the 2-way interaction (Temp*Light) are significant."]
["Factorial Plots","Title","This tool can generate three types of factorial plots to help you visualize the effects, namely the main effects, interactions and cube."]
[null,"Details","They can be used to help you visualize how the response relates to one or more factors.\n\nThe main effects plot charts the means of factor levels for each factor of 1 to 11 factors. Center points are also plotted if included. This plot can be used to compare the strength of the main effects across factors. \n\nThe interactions plot charts the means for each combination of factor levels for a pair of factors of 2 to 11 factors. Center points are also plotted if included. If more than two factors are included, a matrix of interaction plots is generated. In general, an interaction between factors can be identified when the change in response value for one factor differs from the change in response value for the other factor.\n\nThe cube plots charts the means of each factor level combination for 3 to 8 factors. "]
[null,"How to","• Choose ProcessMA > DOE > Factorial Plots \n• In Response, select the column containing the response data (Numeric)\n• In Main Effects - Factors, select the columns containing the factor levels for Main Effects Plot (Between 2 to 11 factors) \n• In Interactions - Factors, select the columns containing the factor levels for Interactions Plot (Between 2 factors to 11 factors) \n• In Cube - Factors, select the columns containing the factor levels (Between 3 to 8 factors)\n• Click OK"]
[null,"Example","You want to investigate how temperature, intensity of light and type of catalyst affect the growth of organisms. You created a full factorial design for three factors and with three replicates. You ran the experiments and recorded the data. You want to use Factorial Plots to visualise the effects.\nRefer to Create Factorial Design help file to create a design for analysis\n• Choose ProcessMA > DOE > Factorial Plots \n• In Response, select H - Response \n• In Main Effects - Factors, select E - Temp, F - Light, G - Catalyst \n• In Interactions - Factors, select E - Temp, F - Light, G - Catalyst \n• In Cube - Factors, select E - Temp, F - Light, G - Catalyst \n• Click OK"]
[null,"Results","The Main Effects Plot suggests that growth increases for the high levels of all three factors and the Catalyst effects are small. From the Interactions Plot, there seems to be no significant interactions among factors. The Cube Plot shows the mean response value for various combinations of factor levels."]
["CONTROL CHARTS"]
["VARIABLE-SUBGROUP"]
["Xbar-R Chart","Title","The Xbar-R chart consist of is a control chart of subgroup means and a control chart of subgroup ranges."]
[null,"Details","It is used to track both the process level and process variation at the same time, and detect signs of special causes. The process standard deviation is estimated using pooled standard deviation as default."]
[null,"How to","• Choose ProcessMA > Control Charts > Variables Charts for Subgroups > Xbar-R\n• In Variable, select the column containing the data (Numeric) \n• In Subgroup, select the column containing subgroup indicators (Optional, >=2 distinct values) \n• In Constant Subgroup Size, enter the subgroup size if it is constant (Optional, Integer, >=2) \n• In Historical Mean, enter the population proportion, otherwise it will be estimated from the sample (Optional, Numeric) \n• In Historical Standard Deviation, enter the population standard deviation, otherwise it will be estimated from the data (Optional, Numeric, >0)\n• In Control Limit Multiples, enter the position to draw the upper and lower control limits. Multiple entries must be separated by commas (Optional, Numeric, >0, Up to 3 multiples) \n• In Xbar-Lower Limit Bound, enter the bound on the lower control limit for the Xbar chart (Optional, Numeric) \n• In Xbar-Upper Limit Bound, enter the bound on the upper control limit for the Xbar chart (Optional, Numeric)\n• In R-Lower Limit Bound, enter the bound on the lower control limit for the R chart (Optional, Numeric) \n• In R-Upper Limit Bound, enter the bound on the upper control limit for the R chart (Optional, Numeric)\n• In Phase, select the column containing the phase indicators (Optional, >=2 distinct values) \n• In Method, choose the method of estimating sigma\n• Check the various checkboxes to perform respective tests \n• Click OK"]
[null,"Example","You are the branch manager of a bank and you need to ensure that time customers spent waiting in the queue is in control. For each day you took 5 measurements on the waiting time. You want to generate a Xbar-R Chart to track the process level and variation.\n• Open data worksheet by choosing ProcessMA > Tools > Data\n• Choose ProcessMA > Control Charts > Variables Charts for Subgroups > Xbar-R\n• In Variable, select V - Waiting Time \n• In Constant Subgroup Size, enter 5\n• Click OK"]
[null,"Results","The ninth point of the Xbar Chart lies outside of the control limit suggesting a possible special cause. The points in the R Chart is random and within the control limit, suggesting that the variation of the process is stable."]
["Xbar-S Chart","Title","The Xbar-S Chart consists of is a control chart of subgroup means and a control chart of subgroup standard deviations."]
[null,"Details","It is used to track both the process level and process variation at the same time, and detect signs of special causes. The process standard deviation is estimated using pooled standard deviation as default."]
[null,"How to","• Choose ProcessMA > Control Charts > Variables Charts for Subgroups > XBar-S\n• In Variable, select the column containing the data (Numeric) \n• In Subgroup, select the column containing subgroup indicators (Optional, >=2 distinct values) \n• In Constant Subgroup Size, enter the subgroup size if it is constant (Optional, Integer, >=2) \n• In Historical Mean, enter the population proportion, otherwise it will be estimated from the sample (Optional, Numeric) \n• In Historical Standard Deviation, enter the population standard deviation, otherwise it will be estimated from the data (Optional, Numeric, >0)\n• In Control Limit Multiples, enter the position to draw the upper and lower control limits. Multiple entries must be separated by commas (Optional, Numeric, >0, Up to 3 multiples) \n• In Xbar-Lower Limit Bound, enter the bound on the lower control limit for the Xbar chart (Optional, Numeric) \n• In Xbar-Upper Limit Bound, enter the bound on the upper control limit for the Xbar chart (Optional, Numeric)\n• In S-Lower Limit Bound, enter the bound on the lower control limit for the S chart (Optional, Numeric) \n• In S-Upper Limit Bound, enter the bound on the upper control limit for the S chart (Optional, Numeric)\n• In Phase, select the column containing the phase indicators (Optional, >=2 distinct values) \n• In Method, choose the method of estimating sigma\n• Check the various checkboxes to perform respective tests \n• Click OK"]
[null,"Example","You are the branch manager of a bank and you need to ensure that time customers spent waiting in the queue is in control. For each day you took 10 measurements on the waiting time. You want to generate a Xbar-S Chart to track the process level and variation.\n• Open data worksheet by choosing ProcessMA > Tools > Data\n• Choose ProcessMA > Control Charts > Variables Charts for Subgroups > Xbar-S\n• In Variable, select V - Waiting Time \n• In Constant Subgroup Size, enter 10\n• Click OK"]
[null,"Results","The fifth point of the Xbar Chart lies outside of the control limit suggesting a possible special cause. The points in the S Chart is random and within the control limit, suggesting that the variation of the process is stable."]
["I-MR-R/S Chart","Title","The I-MR-R/S uses both between-subgroup and within-subgroup variations to generate three control charts, the individuals, moving range and R or S charts."]
[null,"Details","It is useful when the overall process variation is due to both between subgroup variation and random error.\n\nThe individuals chart plots the subgroup means as individual values to remove variation within subgroup and is used to track process level. The moving range chart plots the subgroup means using a moving range to remove variation within subgroup variation and is used to track process variation between subgroups. The R or S chart plots on the other hand uses variation within subgroup to track process variation within subgroups. The R chart is used when the subgroup size is small or Rbar is used to estimate process variation. The S chart is used when subgroup size is larger or when Sbar is used to estimate process variation. "]
[null,"How to","• Choose ProcessMA > Control Charts > Variables Charts for Subgroups > I-MR-R/S\n• In Variable, select the column containing the data (Numeric) \n• In Subgroup, select the column containing subgroup indicators (Optional, >=2 distinct values) \n• In Constant Subgroup Size, enter the subgroup size if it is constant (Optional, Integer, >=2) \n• In Mean, enter the population proportion, otherwise it will be estimated from the sample (Optional, Numeric) \n• In Std Dev Between Subgroups, enter the standard deviation between subgroups, otherwise it will be estimated from the data (Optional, Numeric, >0)\n• In Std Dev Within Subgroups, enter the standard deviation within subgroups, otherwise it will be estimated from the data (Optional, Numeric, >0)\n• In Control Limit Multiples, enter the position to draw the upper and lower control limits. Multiple entries must be separated by commas (Optional, Numeric, >0, Up to 3 multiples) \n• In I-Lower Limit Bound, enter the bound on the lower control limit for the individuals chart (Optional, Numeric) \n• In I-Upper Limit Bound, enter the bound on the upper control limit for the individuals chart (Optional, Numeric)\n• In MR-Lower Limit Bound, enter the bound on the lower control limit for the MR chart (Optional, Numeric) \n• In MR-Upper Limit Bound, enter the bound on the upper control limit for the MR chart (Optional, Numeric)\n• In R/S-Lower Limit Bound, enter the bound on the lower control limit for the R/S chart (Optional, Numeric) \n• In R/S-Upper Limit Bound, enter the bound on the upper control limit for the R/S chart (Optional, Numeric)\n• In Phase, select the column containing the phase indicators (Optional, >=2 distinct values) \n• In Method (Subgroup>1), choose the method of estimating sigma when subgroup size is greater than 1 \n• In Method (Subgroup=1), choose the method of estimating sigma when subgroup size is equals to 1\n• In Moving Range Length, enter the number of observations used to calculate the moving range (Integer, >=2)\n• Check the various checkboxes to perform respective tests \n• Click OK"]
[null,"Example","You are the operations manager in a production plant. You need to ensure that the dimensions of the parts manufactured are in control and within specifications. You took measurements of 10 parts from each of the 8 production lines. You want to generate a I-MR-R/S Chart to monitor the process.\n• Open data worksheet by choosing ProcessMA > Tools > Data\n• Choose ProcessMA > Control Charts > Variables Charts for Subgroups > I-MR-R/S\n• In Variable, select W - Parts \n• In Subgroup, select X - Subgroup \n• Click OK"]
[null,"Results","The process is in control within and between subgroups (production lines)."]
["Xbar Chart","Title","The Xbar Chart is a control chart of subgroup means."]
[null,"Details","It is used to track the process level and detect signs of special causes. The process standard deviation is estimated using pooled standard deviation as default."]
[null,"How to","• Choose ProcessMA > Control Charts > Variables Charts for Subgroups > Xbar\n• In Variable, select the column containing the data (Numeric) \n• In Subgroup, select the column containing subgroup indicators (Optional, >=2 distinct values) \n• In Constant Subgroup Size, enter the subgroup size if it is constant (Optional, Integer, >=2) \n• In Historical Mean, enter the population proportion, otherwise it will be estimated from the sample (Optional, Numeric, >0 & <1) \n• In Historical Standard Deviation, enter the population standard deviation, otherwise it will be estimated from the data (Optional, Numeric, >0)\n• In Control Limit Multiples, enter the position to draw the upper and lower control limits. Multiple entries must be separated by commas (Optional, Numeric, >0, Up to 3 multiples) \n• In Lower Limit Bound, enter the bound on the lower control limit (Optional, Numeric) \n• In Upper Limit Bound, enter the bound on the upper control limit (Optional, Numeric)\n• In Phase, select the column containing the phase indicators (Optional, >=2 distinct values) \n• In Method, choose the method of estimating sigma\n• Check the various checkboxes to perform respective tests \n• Click OK"]
[null,"Example","You are the branch manager of a bank and you need to ensure that time customers spent waiting in the queue is in control. For each day you took 10 measurements on the waiting time. You want to generate a Xbar Chart to track the process level.\n• Open data worksheet by choosing ProcessMA > Tools > Data\n• Choose ProcessMA > Control Charts > Variables Charts for Subgroups > Xbar\n• In Variable, select V - Waiting Time\n• In Constant Subgroup Size, enter 10 \n• Click OK"]
[null,"Results","The fifth point lies outside of the control limit suggesting a possible special cause."]
["R Chart","Title","The R Chart is a control chart of subgroup ranges. It is used to track the process variation and detect signs of special causes."]
[null,"Details","It is suitable for sample sizes 8 or less. For bigger sample sizes, the S Chart may be more appropriate. The process standard deviation is estimated using pooled standard deviation as default."]
[null,"How to","• Choose ProcessMA > Control Charts > Variables Charts for Subgroups > R\n• In Variable, select the column containing the data (Numeric) \n• In Subgroup, select the column containing subgroup indicators (Optional, >=2 distinct values) \n• In Constant Subgroup Size, enter the subgroup size if it is constant (Optional, Integer, >=2) \n• In Historical Standard Deviation, enter the population standard deviation, otherwise it will be estimated from the data (Optional, Numeric, >0)\n• In Control Limit Multiples, enter the position to draw the upper and lower control limits. Multiple entries must be separated by commas (Optional, Numeric, >0, Up to 3 multiples) \n• In Lower Limit Bound, enter the bound on the lower control limit (Optional, Numeric) \n• In Upper Limit Bound, enter the bound on the upper control limit (Optional, Numeric)\n• In Phase, select the column containing the phase indicators (Optional, >=2 distinct values) \n• In Method, choose the method of estimating sigma\n• Check the various checkboxes to perform respective tests \n• Click OK"]
[null,"Example","You are the branch manager of a bank and you need to ensure that time customers spent waiting in the queue is in control. For each day you took 5 measurements on the waiting time. You want to generate a R Chart to track the variation.\n• Open data worksheet by choosing ProcessMA > Tools > Data\n• Choose ProcessMA > Control Charts > Variables Charts for Subgroups > R\n• In Variable, select V - Waiting Time\n• In Constant Subgroup Size, enter 5\n• Click OK"]
[null,"Results","You are the branch manager of a bank and you need to ensure that time customers spent waiting in the queue is in control. For each day you took 5 measurements on the waiting time. You want to generate a R Chart to track the variation."]
["S Chart","Title","The S Chart is a control chart of subgroup standard deviations. It is used to track the process variation and detect signs of special causes."]
[null,"Details","It is suitable for sample sizes larger than 8. For smaller sample sizes, the R Chart may be more appropriate. The process standard deviation is estimated using pooled standard deviation as default."]
[null,"How to","• Choose ProcessMA > Control Charts > Variables Charts for Subgroups > S \n• In Variable, select the column containing the data (Numeric) \n• In Subgroup, select the column containing subgroup indicators (Optional, >=2 distinct values) \n• In Constant Subgroup Size, enter the subgroup size if it is constant (Optional, Integer, >=2) \n• In Historical Standard Deviation, enter the population standard deviation, otherwise it will be estimated from the data (Optional, Numeric, >0)\n• In Control Limit Multiples, enter the position to draw the upper and lower control limits. Multiple entries must be separated by commas (Optional, Numeric, >0, Up to 3 multiples) \n• In Lower Limit Bound, enter the bound on the lower control limit (Optional, Numeric) \n• In Upper Limit Bound, enter the bound on the upper control limit (Optional, Numeric)\n• In Phase, select the column containing the phase indicators (Optional, >=2 distinct values) \n• In Method, choose the method of estimating sigma\n• Check the various checkboxes to perform respective tests \n• Click OK"]
[null,"Example","You are the branch manager of a bank and you need to ensure that time customers spent waiting in the queue is in control. For each day you took 10 measurements on the waiting time. You want to generate a S Chart to track the variation.\n• Open data worksheet by choosing ProcessMA > Tools > Data\n• Choose ProcessMA > Control Charts > Variables Charts for Subgroups > S\n• In Variable, select V - Waiting Time\n• In Constant Subgroup Size, enter 10\n• Click OK"]
[null,"Results","The process is stable as the data points are randomly distributed and lie within the control limits."]
["Zone Chart","Title","The Zone Chart is similar to the Xbar or individuals Chart. It plots a cumulative score based on zones."]
[null,"Details","It is useful because ‘out-of-control’ is easy to identify, which is when cumulative score is greater than 8."]
[null,"How to","• Choose ProcessMA > Control Charts > Variables Charts for Subgroups > Zone \n• In Variable, select the column containing the data (Numeric) \n• In Subgroup, select the column containing subgroup indicators (Optional, >=2 distinct values) \n• In Constant Subgroup Size, enter the subgroup size if it is constant (Optional, Integer, >=2) \n• In Historical Mean, enter the population proportion, otherwise it will be estimated from the sample (Optional, Numeric) \n• In Historical Standard Deviation, enter the population standard deviation, otherwise it will be estimated from the data (Optional, Numeric, >0)\n• In Control Limit Multiples, enter the position to draw the upper and lower control limits. Multiple entries must be separated by commas (Optional, Numeric, >0, Up to 3 multiples) \n• In Lower Limit Bound, enter the bound on the lower control limit (Optional, Numeric) \n• In Upper Limit Bound, enter the bound on the upper control limit (Optional, Numeric)\n• In Phase, select the column containing the phase indicators (Optional, >=2 distinct values) \n• In Method (Subgroup>1), choose the method of estimating sigma when subgroup size is greater than 1 \n• In Method (Subgroup=1), choose the method of estimating sigma when subgroup size is equals to 1\n• In Moving Range Length, enter the number of observations used to calculate the moving range (Integer, >=2)\n• In Zone 1 (Std Dev <1), enter the weights you want to assign to points in Zone 1\n• In Zone 2 (Std Dev <2), enter the weights you want to assign to points in Zone 2 \n• In Zone 3 (Std Dev <3), enter the weights you want to assign to points in Zone 3 \n• In Zone 4 (Std Dev >3), enter the weights you want to assign to points in Zone 4 \n• Check Reset Score After Each Signal, if you want to reset the cumulative score to zero following each out of control signal\n• Click OK"]
[null,"Example","You operate a delivery service and you want to ensure that parcels are delivered to your customers on time. You recorded the delivery times for 5 parcels to the same area for the past 10 days. You want to run the Zone Chart to evaluate the situation.\n• Open data worksheet by choosing ProcessMA > Tools > Data\n• Choose ProcessMA > Control Charts > Variables Charts for Subgroups > Zone \n• In Variable, select AB - Delivery Time\n• In Constant Subgroup Size, enter 5 \n• Click OK "]
[null,"Results","Several points have cumulative scores equals or greater than 8 which suggest the process is out of control."]
["VARIABLE-INDIVIDUALS"]
["I-MR Chart","Title","The I-MR chart is made up of an individuals Chart and Moving Range Chart."]
[null,"Details","It allows you to track both process level and process variation at the same time and detect signs of special causes. The process standard deviation is estimated using average moving range with moving range equals to 2 as default"]
[null,"How to","• Choose ProcessMA > Control Charts > Variables Charts for Individuals > I-MR\n• In Variable, select the column containing the data (Positive integer) \n• In Historical Mean, enter the population mean, otherwise it will be estimated by the sample mean (Optional, Numeric)\n• In Historical Standard Deviation, enter the population standard deviation, otherwise it will be estimated from the data (Optional, Numeric, >0)\n• In Control Limit Multiples, enter the position to draw the upper and lower control limits. Multiple entries must be separated by commas (Optional, Numeric, >0, Up to 3 multiples) \n• In I-Lower Limit Bound, enter the bound on the lower control limit for the individuals chart (Optional, Numeric) \n• In I-Upper Limit Bound, enter the bound on the upper control limit for the individuals chart (Optional, Numeric)\n• In MR-Lower Limit Bound, enter the bound on the lower control limit for the moving range chart (Optional, Numeric)\n• In MR-Upper Limit Bound, enter the bound on the upper control limit for the moving range chart (Optional, Numeric)\n• In Phase, select the column containing the phase indicators (Optional, >=2 distinct values) \n• In Method, choose the method of estimating sigma\n• In Moving Range Length, enter the number of observations used to calculate the moving range (Integer, >=2) \n• Check the various checkboxes to perform respective tests \n• Click OK"]
[null,"Example","You are the manager of a technical help division. There have been complains that response time were getting slow and erratic. You collected several measurements on response time and you want to run the I-MR Chart to evaluate the situation.\n• Open data worksheet by choosing ProcessMA > Tools > Data\n• Choose ProcessMA > Control Charts > Variables Charts for Individuals > I-MR\n• In Variable, select U - Response Time \n• Click OK"]
[null,"Results","The ninth point of the Individuals Chart lies outside the upper control limit which suggests a possible special cause on the process level. The process variation is stable as the data points are randomly distributed and lie within the control limits of the Moving Range Chart."]
["Z-MR Chart","Title","The Z-MR Chart is made up of a control chart of standardised individual observations and the Moving Range Chart."]
[null,"Details","It allows you to track both process level and process variation at the same time. The Z-MR is useful for processes with insufficient data on each run to give a good estimate of process parameters. Individual observations are therefore standardised so that data collected from different runs can be evaluated on the same control chart."]
[null,"How to","• Choose ProcessMA > Control Charts > Variables Charts for Individuals > Z-MR\n• In Variable, select the column containing the data (Numeric) \n• In Part Indicators , select the column containing part indicators (>=2 distinct values) \n• In Control Limit Multiples, enter the position to draw the upper and lower control limits. Multiple entries must be separated by commas (Optional, Numeric, >0, Up to 3 multiples) \n• In Lower Limit Bound, enter the bound on the lower control limit (Optional, Numeric) \n• In Upper Limit Bound, enter the bound on the upper control limit (Optional, Numeric)\n• In Group Method, choose the grouping method of estimating sigma\n• In Method, choose the method of estimating sigma when subgroup size is equals to 1\n• In Moving Range Length, enter the number of observations used to calculate the moving range (Integer, >=2)\n• Click OK"]
[null,"Example","You work in a mill and you are in-charge of quality control. The mill cuts wood into specific dimensions and dimension settings are changed according to customer’s order. You want to use the Z-MR Chart to assess if the wood is cut into the correct dimensions. You know that the variation in your process is dependent on the type of wood used.\n• Open data worksheet by choosing ProcessMA > Tools > Data\n• Choose ProcessMA > Control Charts > Variables Charts for Individuals > Z-MR\n• In Variable, select Z - Dimension\n• In Part Indicators , select AA - Wood\n• Click OK "]
["Individuals Chart","Title","The Individuals Chart is a control chart of individual observations."]
[null,"Details","It is used to track the process level and detect signs of special causes when subgroup size is equals to 1. The process standard deviation is estimated using average moving range with moving range equals to 2 as default."]
[null,"How to","• Choose ProcessMA > Control Charts > Variables Charts for Individuals > Individuals\n• In Variable, select the column containing the data (Positive integer) \n• In Historical Mean, enter the population mean, otherwise it will be estimated by the sample mean (Optional, Numeric)\n• In Historical Standard Deviation, enter the population standard deviation, otherwise it will be estimated from the data (Optional, Numeric, >0)\n• In Control Limit Multiples, enter the position to draw the upper and lower control limits. Multiple entries must be separated by commas (Optional, Numeric, >0, Up to 3 multiples) \n• In Lower Limit Bound, enter the bound on the lower control limit (Optional, Numeric) \n• In Upper Limit Bound, enter the bound on the upper control limit (Optional, Numeric)\n• In Phase, select the column containing the phase indicators (Optional, >=2 distinct values) \n• In Method, choose the method of estimating sigma\n• In Moving Range Length, enter the number of observations used to calculate the moving range (Integer, >=2) \n• Check the various checkboxes to perform respective tests \n• Click OK"]
[null,"Example","You are the manager of a technical help division. There have been complains that response time were getting slow and erratic. You collected several measurements on response time and you want to run the I-MR Chart to evaluate the situation.\n• Open data worksheet by choosing ProcessMA > Tools > Data\n• Choose ProcessMA > Control Charts > Variables Charts for Individuals > Individuals\n• In Variable, select U - Response Time \n• Click OK"]
[null,"Results","The ninth point lies outside the upper control limit which suggests a possible special cause. Further investigation is required and it is possible that it is the cause of that complaint."]
["Moving Range Chart","Title","The Moving Range Chart is a control chart of moving ranges."]
[null,"Details","Moving ranges are range value of preceding successive observations. It is used to track the process variation and detect signs of special causes with subgroup size is equals to 1. The process standard deviation is estimated using average moving range with moving range equals to 2 as default."]
[null,"How to","• Choose ProcessMA > Control Charts > Variables Charts for Individuals > Moving Range\n• In Variable, select the column containing the data (Positive integer) \n• In Historical Standard Deviation, enter the population standard deviation, otherwise it will be estimated from the data (Optional, Numeric, >0)\n• In Control Limit Multiples, enter the position to draw the upper and lower control limits. Multiple entries must be separated by commas (Optional, Numeric, >0, Up to 3 multiples) \n• In Lower Limit Bound, enter the bound on the lower control limit (Optional, Numeric) \n• In Upper Limit Bound, enter the bound on the upper control limit (Optional, Numeric)\n• In Phase, select the column containing the phase indicators (Optional, >=2 distinct values) \n• In Method, choose the method of estimating sigma\n• In Moving Range Length, enter the number of observations used to calculate the moving range (Integer, >=2) \n• Check the various checkboxes to perform respective tests \n• Click OK"]
[null,"Example","You are the manager of a technical help division. There have been complains that response time were getting slow and erratic. You collected several measurements on response time and you want to run the I-MR Chart to evaluate the situation.\n• Open data worksheet by choosing ProcessMA > Tools > Data\n• Choose ProcessMA > Control Charts > Variables Charts for Individuals > Moving Range\n• In Variable, select U - Response Time \n• Click OK"]
[null,"Results","The process is stable as the data points are randomly distributed and lie within the control limits."]
["ATTRIBUTE"]
["P Chart","Title","The P Chart is a control chart used to track the proportion defective (number of defectives divided by the subgroup size) and detect signs of special causes."]
[null,"Details","The data is assumed to follow a Binomial distribution."]
[null,"How to","• Choose ProcessMA > Control Charts > Attributes Charts > P \n• In Variable, select the column containing the data (Positive integer) \n• In Subgroup Sizes , select the column containing subgroup sizes (Optional, Positive integer, >=Variable) \n• In Constant Subgroup Size , enter the subgroup size if it is constant (Positive integer, >=Variable) \n• In Proportion, enter the population proportion, otherwise it will be estimated from the sample (Optional, Numeric, >0 & <1) \n• In Control Limit Multiples, enter the position to draw the upper and lower control limits. Multiple entries must be separated by commas (Optional, Numeric, >0, Up to 3 multiples) \n• In Lower Limit Bound, enter the bound on the lower control limit (Optional, Numeric) \n• In Upper Limit Bound, enter the bound on the upper control limit (Optional, Numeric)\n• In Phase, select the column containing the phase indicators (Optional, >=2 distinct values) \n• Check the various checkboxes to perform respective tests \n• Click OK"]
[null,"Example","You work in a paper manufacturing plant and you need the control the quality of the paper. For each batch, you inspect a certain quantity to make sure that the papers are ‘white enough’ for quality control. You want to use the NP chart to help you monitor.\n• Open data worksheet by choosing ProcessMA > Tools > Data\n• Choose ProcessMA > Control Charts > Attributes Charts > P \n• In Variable, select S - Stained \n• In Subgroup Sizes , select T - Sampled \n• Click OK\n"]
[null,"Results","Sample 20 is outside the control limit and you may wish to investigate that batch for quality issues."]
["NP Chart","Title","The P Chart is a control chart used to track the number of defectives and detect signs of special causes. "]
[null,"Details","The NP chart is normally used when the subgroup size is constant. The data is assumed to follow a Binomial distribution."]
[null,"How to","• Choose ProcessMA > Control Charts > Attributes Charts > NP\n• In Variable, select the column containing the data (Positive integer) \n• In Subgroup Sizes , select the column containing subgroup sizes (Optional, Positive integer, >=Variable) \n• In Constant Subgroup Size , enter the subgroup size if it is constant (Positive integer, >=Variable)\n• In Proportion, enter the population proportion, otherwise it will be estimated from the sample (Optional, Numeric, >0 & <1) \n• In Control Limit Multiples, enter the position to draw the upper and lower control limits. Multiple entries must be separated by commas (Optional, Numeric, >0, Up to 3 multiples) \n• In Lower Limit Bound, enter the bound on the lower control limit (Optional, Numeric) \n• In Upper Limit Bound, enter the bound on the upper control limit (Optional, Numeric)\n• In Phase, select the column containing the phase indicators (Optional, >=2 distinct values) \n• Check the various checkboxes to perform respective tests \n• Click OK\n\n "]
[null,"Example","You work in a paper manufacturing plant and you need the control the quality of the paper. For each batch, you inspect a certain quantity to make sure that the papers are ‘white enough’ for quality control. You want to use the NP chart to help you monitor.\n• Open data worksheet by choosing ProcessMA > Tools > Data\n• Choose ProcessMA > Control Charts > Attributes Charts > NP\n• In Variable, select S - Stained \n• In Subgroup Sizes , select T - Sampled \n• Click OK"]
[null,"Results","Sample 20 is outside the control limit and you may want to investigate that production batch for quality issues."]
["C Chart","Title","The C Chart is a control chart used to track the number of defects and detect signs of special causes. "]
[null,"Details","To use C Chart, the subgroup size must be constant. The data is assumed to follow a Poisson distribution and the average number of defects is estimated from the data."]
[null,"How to","• Choose ProcessMA > Control Charts > Attributes Charts > C \n• In Variable, select the column containing the data (Positive integer) \n• In Historical Mean, enter the population mean, otherwise it will be estimated by the sample mean (Optional, Numeric)\n• In Control Limit Multiples, enter the position to draw the upper and lower control limits. Multiple entries must be separated by commas (Optional, Numeric, >0, Up to 3 multiples) \n• In Lower Limit Bound, enter the bound on the lower control limit (Optional, Numeric) \n• In Upper Limit Bound, enter the bound on the upper control limit (Optional, Numeric)\n• In Phase, select the column containing the phase indicators (Optional, >=2 distinct values) \n• Check the various checkboxes to perform respective tests \n• Click OK"]
[null,"Example","You work in a paper manufacturing plant and you need to control the quality of the paper. For each batch, you inspected 100 pieces of paper to make sure that they are not stained. You want to use the C Chart to help you monitor the quality.\n• Open data worksheet by choosing ProcessMA > Tools > Data\n• Choose ProcessMA > Control Charts > Attributes Charts > C \n• In Variable, select S - Stained \n• Click OK"]
[null,"Results","The process is stable as the data points are randomly distributed and lie within the control limits."]
["U Chart","Title","The U Chart is a control chart used to track the number of defects per unit sampled and detect signs of special causes. "]
[null,"Details","The U Chart is useful when the subgroup size varies. The data is assumed to follow a Poisson distribution and the average number of defects is estimated from the data."]
[null,"How to","• Choose ProcessMA > Control Charts > Attributes Charts > U \n• In Variable, select the column containing the data (Positive integer) \n• In Subgroup Sizes , select the column containing subgroup sizes (Optional, Positive integer, >=Variable) \n• In Constant Subgroup Size , enter the subgroup size if it is constant (Positive integer, >=Variable)\n• In Historical Mean, enter the population mean, otherwise it will be estimated by the sample mean (Optional, Numeric) \n• In Control Limit Multiples, enter the position to draw the upper and lower control limits. Multiple entries must be separated by commas (Optional, Numeric, >0, Up to 3 multiples) \n• In Lower Limit Bound, enter the bound on the lower control limit (Optional, Numeric) \n• In Upper Limit Bound, enter the bound on the upper control limit (Optional, Numeric)\n• In Phase, select the column containing the phase indicators (Optional, >=2 distinct values) \n• Check the various checkboxes to perform respective tests \n• Click OK\n"]
[null,"Example","You work in a paper manufacturing plant and you need the control the quality of the paper. For each batch, you inspect a certain quantity to make sure that the papers are ‘white enough’ for quality control. You want to use the U chart to help you monitor.\n• Open data worksheet by choosing ProcessMA > Tools > Data\n• Choose ProcessMA > Control Charts > Attributes Charts > U \n• In Variable, select S - Stained \n• In Subgroup Sizes , select T - Sampled \n• Click OK"]
[null,"Results","Sample 20 is outside the control limit and you may want to investigate that batch for quality issues."]
["TIME-WEIGHTED"]
["Moving Average Chart","Title","The Moving Average Chart is a control chart of moving averages (of individuals or subgroup means)."]
[null,"Details","It is used to track the process level and detect signs of special causes. Moving Average chart uses unweighted moving averages and therefore it is generally not as popular as the EWMA chart which weight the observations. \n\nMoving averages are averages of a number (default length of MA = 3) of consecutive observations or subgroup means. If your data is in subgroups, the process standard deviation is estimated using pooled standard deviation as default. If your data is individual observations (subgroup size = 1), the process standard deviation is estimated using average moving range with moving range equals to 2 as default. "]
[null,"How to","• Choose ProcessMA > Control Charts > Time-Weighted Charts > Moving Average\n• In Variable, select the column containing the data (Numeric) \n• In Subgroup, select the column containing subgroup indicators (Optional, >=2 distinct values) \n• In Constant Subgroup Size, enter the subgroup size if it is constant (Optional, Integer, >=2) \n• In Moving Average Length, enter the number of observations used to calculate the moving average (Integer, >=2)\n• In Historical Mean, enter the population proportion, otherwise it will be estimated from the sample (Optional, Numeric) \n• In Historical Standard Deviation, enter the population standard deviation, otherwise it will be estimated from the data (Optional, Numeric, >0)\n• In Control Limit Multiples, enter the position to draw the upper and lower control limits. Multiple entries must be separated by commas (Optional, Numeric, >0, Up to 3 multiples) \n• In Lower Limit Bound, enter the bound on the lower control limit (Optional, Numeric) \n• In Upper Limit Bound, enter the bound on the upper control limit (Optional, Numeric)\n• In Phase, select the column containing the phase indicators (Optional, >=2 distinct values) \n• In Method (Subgroup>1), choose the method of estimating sigma when subgroup size is greater than 1 \n• In Method (Subgroup=1), choose the method of estimating sigma when subgroup size is equals to 1\n• In Moving Range Length, enter the number of observations used to calculate the moving range (Integer, >=2)\n• Click OK"]
[null,"Example","You collected cycle time data for application approval. You want to monitor the process using a Moving Average Chart.\n• Open data worksheet by choosing ProcessMA > Tools > Data\n• Choose ProcessMA > Control Charts > Time-Weighted Charts > Moving Average\n• In Variable, select Y - Approval Time \n• In Constant Subgroup Size, enter 1\n• Click OK"]
["EWMA Chart","Title","The EWMA chart is a control chart of exponentially weighted moving averages (of individuals or subgroup means)."]
[null,"Details","Each point contains a weighted effect from all the previous points. It can be used to track small shifts away from the target.\n\nMoving averages are averages of a number (default length of MA = 3) of consecutive observations or subgroup means. If your data is in subgroups, the process standard deviation is estimated using pooled standard deviation as default. If your data is individual observations (subgroup size = 1), the process standard deviation is estimated using average moving range with moving range equals to 2 as default."]
[null,"How to","• Choose ProcessMA > Control Charts > Time-Weighted Charts > EWMA \n• In Variable, select the column containing the data (Numeric) \n• In Subgroup, select the column containing subgroup indicators (Optional, >=2 distinct values) \n• In Constant Subgroup Size, enter the subgroup size if it is constant (Optional, Integer, >=2) \n• In Weight, enter the weight for EWMA (Numeric, >0 & <1) \n• In Historical Mean, enter the population proportion, otherwise it will be estimated from the sample (Optional, Numeric) \n• In Historical Standard Deviation, enter the population standard deviation, otherwise it will be estimated from the data (Optional, Numeric, >0)\n• In Control Limit Multiples, enter the position to draw the upper and lower control limits. Multiple entries must be separated by commas (Optional, Numeric, >0, Up to 3 multiples) \n• In Lower Limit Bound, enter the bound on the lower control limit (Optional, Numeric) \n• In Upper Limit Bound, enter the bound on the upper control limit (Optional, Numeric)\n• In Phase, select the column containing the phase indicators (Optional, >=2 distinct values) \n• In Method (Subgroup>1), choose the method of estimating sigma when subgroup size is greater than 1 \n• In Method (Subgroup=1), choose the method of estimating sigma when subgroup size is equals to 1\n• In Moving Range Length, enter the number of observations used to calculate the moving range (Integer, >=2)\n• Click OK"]
[null,"Example","You collected cycle time (days) data for application approval. You want to monitor the process using a EWMA chart.\n• Open data worksheet by choosing ProcessMA > Tools > Data\n• Choose ProcessMA > Control Charts > Time-Weighted Charts > EWMA\n• In Variable, select Y - Approval Time \n• In Constant Subgroup Size, enter 1\n• Click OK"]
["Define Test of Special Causes","Title","Each of the eight tests for special causes detects a specific pattern in the data and such occurrence indicates a special cause for the variation."]
[null,"Details","You can change the test parameter to adjust test sensitivity.\nTest 1: One point is more than 3s from center line.\nTest 2: Nine consecutive points Nine on same side of center line\nTest 3: Six consecutive points, all increasing or all decreasing\nTest 4: Fourteen consecutive points, alternating up and down\nTest 5: Two out of three consecutive points more than 2s from center line (same side)\nTest 6: Four out of five consecutive points more than 1s from center line (same side)\nTest 7: Fifteen consecutive points within 1s of center line (either side)\nTest 8: Eight consecutive points more than 1s from center line (either side)"]
[null,"How to","Choose ProcessMA > Control Charts > Define Tests \n• Enter k values for the respective tests (integer, between allowable range) \n• Click OK to save changes\n• Click Default to reset k values to original setting\n• Click Cancel to close dialog box without saving "]
["Box-Cox Transformation","Title","Box-Cox transformation can be used to transform non-normal data into normal data for usage in control charts or instances where normal data is required."]
[null,"Details","You can specify a known lambda to transform the data or let ProcessMA estimate for you. The transformed data is stored in Column AB. The graphical output can be used to select an appropriate lambda for practical purposes. For example, if the estimated lambda is 0.49, it can may be easier to use a square root without losing must accuracy. "]
[null,"How to","• Choose ProcessMA > Control Charts > Box-Cox Transformation\n• In Variable, select the column containing the data (Numeric) \n• In Subgroup, select the column containing subgroup indicators (Optional, >=2 distinct values) \n• In Constant Subgroup Size, enter the subgroup size if it is constant (Optional, Integer, >=2) \n• In Specify Lambda, enter the specific lambda to transform the data (Optional, Numeric, >-5& <5) \n• Click OK"]
[null,"Example","You have some data in subgroup sizes of 10. The data is not normal and with outliers. You want transform the data for further analysis.\n• Open data worksheet by choosing ProcessMA > Tools > Data\n• Choose ProcessMA > Control Charts > Box-Cox Transformation\n• In Variable, select AC - Boxcox \n• In Constant Subgroup Size, enter 10 \n• Click OK"]
[null,"Results","To correct for non-normality, you can transform the data to the power of the lambda value at 1.5."]
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["QUALITY TOOLS"]
["CAPABILITY ANALYSIS"]
["Capability Analysis (Normal)","Title","The Capability Analysis (Normal) generates a process capability report containing various capability indices."]
[null,"Details","Capability indices measure how well the process is capable of meeting the specificiations. This tool also generates a histogram of the data with the overall and within normal curves. The histogram helps you to visualize the distribution of you data is whether the process is in control. Capability Analysis (Normal) assumes the data is from a Normal distribution. If you data is not Normal or badly skewed, it may be better to either transform the data using Box-Cox transformation or use Capability Analysis (Weilbull) if the data follows a Weibull Distribution. In order to study the process capability, it is important to make sure that the process is in statistical control first. Make use of the control charts to valid if the process mean (e.g. individuals, Xbar) and the process variation (e.g Moving range, R chart) is stable. \n\nInterpret Capability Indices\n• Cp measures the potential process capability or sometimes referred to as short term \"best case\" performance. It measures how consistent process is performing in relation to the specification limits.  \n• Cpk also measures the potential process capability but unlike Cp, it also take into consideration the location of the process mean in relation to the specification limits. If the process is stable but off-target, Cpk will be smaller than Cp.  \n• Pp measures the overall process capability, sometimes also referred to as long term performance. Therefore, if there are special cause variation present in the process data, Pp will be smaller than Cp.  \n• Ppk also measures the overall process capability but unlike Pp, it also take into consideration the location of the process mean in relation to the specification limits. Similar to the interpretation for Cp and Cpk, If the process is stable but off-target, Ppk will be smaller than Pp. \n• Z is an alternative measure of process capability. In simple terms, Z represents the number of standard deviations between the mean and the specification limit. For 2-sided specification limits, overall Z is smaller than the Z of each specification limit. \n• Observed Performance  The number process output that actually fail the specification limits based on your data. This metric can be expressed in terms of parts per million (PPM) or in percent. \n• Expected Performance  The number of process output that you expect to fail specification limits. This level of performance is what you customer will likely experience. This expectation is based on the distribution (using cumulative distribution function) used to model your data. The expected performance can be expressed in terms of parts per million (PPM) or in percent. "]
[null,"How to","• Choose ProcessMA > Quality Tools > Capability Analysis > Capability Analysis (Normal) \n• In Variable, select the column containing the data (Numeric) \n• In Subgroup, select the column containing subgroup indicators (Optional, >=2 distinct values) \n• In Constant Subgroup Size, enter the subgroup size if it is constant (Optional, Integer, >0) \n• In Lower Specification Limit, enter the lower specification limit (At least one limit is required, Numeric)\n• In Upper Specification Limit, enter the lower specification limit (At least one limit is required, Numeric)\n• In Historical Mean, enter the population proportion, otherwise it will be estimated from the sample (Optional, Numeric) \n• In Historical Standard Deviation, enter the population standard deviation, otherwise it will be estimated from the data (Optional, Numeric, >0)\n• In Target, enter the target value. It is used to calculate Cpm (Optional, Numeric) \n• In Sigma Tolerance, enter the interval (number of standard deviations) to calculate the capability statistics, otherwise 6 standard deviations will be used (Numeric, >0) \n• In Method (Subgroup>1), choose the method of estimating sigma when subgroup size is greater than 1 \n• In Method (Subgroup=1), choose the method of estimating sigma when subgroup size is equals to 1\n• In Moving Range Length, enter the number of observations used to calculate the moving range (Integer, >=2)\n• In Display Capabilities in, choose the method to display capability indices\n• In Display Performance in, choose the method to display performance indices\n• Click OK"]
[null,"Example","You work in manufacturing plant and you need to make sure that the diameter of the parts made is 300mm ± 3mm to meet technical specifications. You collected five samples each day for the last 30 days. You want to perform a capability study to evaluate if the process is capable of meeting the specifications.\n• Open data worksheet by choosing ProcessMA > Tools > Data\n• Choose ProcessMA > Quality Tools > Capability Analysis > Capability Analysis (Normal) \n• In Variable, select D - Diameter \n• In Constant Subgroup Size, enter 10\n• In Lower Specification Limit, enter 298 \n• In Upper Specification Limit, enter 302\n• In Target, enter 300\n• Click OK"]
[null,"Results","The process does not meet the lower and upper specification limits. The process needs to be improved to reduce variation and also centered on the target."]
["Capability Analysis (Between/Within)","Title","The Capability Analysis (Between/Within) generates a process capability report containing various capability indices using both between/within-subgroup variation."]
[null,"Details","Capability indices measure how well the process is capable of meeting the specificiations. It is useful when variation in the data is due to both within and between subgroups. For example, when you collect data, other than the random error within subgroups, there may also be random error between subgroups due to time and environment condition changes. Under these circumstances, the process variation is due to both the between-subgroup variation and the within-subgroup variation.\n\nThis procedure also generates a histogram of the data with the overall and within normal curves. The histogram helps you to visualize the distribution of you data is whether the process is in control. Capability Analysis (Between/Within) assumes the data is from a Normal distribution. If you data is not Normal or badly skewed, it may be better to either transform the data using Box-Cox transformation or use Capability Analysis (Weilbull) if the data follows a Weibull Distribution. In order to study the process capability, it is important to make sure that the process is in statistical control first. Make use of the control charts to valid if the process mean (e.g. individuals, Xbar) and the process variation (e.g Moving range, R chart) is stable. \n\nInterpret Capability Indices\n• Cp measures the potential process capability or sometimes referred to as short term \"best case\" performance. It measures how consistent process is performing in relation to the specification limits.  \n• Cpk also measures the potential process capability but unlike Cp, it also take into consideration the location of the process mean in relation to the specification limits. If the process is stable but off-target, Cpk will be smaller than Cp.  \n• Pp measures the overall process capability, sometimes also referred to as long term performance. Therefore, if there are special cause variation present in the process data, Pp will be smaller than Cp.  \n• Ppk also measures the overall process capability but unlike Pp, it also take into consideration the location of the process mean in relation to the specification limits. Similar to the interpretation for Cp and Cpk, If the process is stable but off-target, Ppk will be smaller than Pp. \n• Z is an alternative measure of process capability. In simple terms, Z represents the number of standard deviations between the mean and the specification limit. For 2-sided specification limits, overall Z is smaller than the Z of each specification limit. \n• Observed Performance  The number process output that actually fail the specification limits based on your data. This metric can be expressed in terms of parts per million (PPM) or in percent. \n• Expected Performance  The number of process output that you expect to fail specification limits. This level of performance is what you customer will likely experience. This expectation is based on the distribution (using cumulative distribution function) used to model your data. The expected performance can be expressed in terms of parts per million (PPM) or in percent. "]
[null,"How to","• Choose ProcessMA > Quality Tools > Capability Analysis > Capability Analysis (Between/Within)\n• In Variable, select the column containing the data (Numeric) \n• In Subgroup, select the column containing subgroup indicators (Optional, >=2 distinct values) \n• In Constant Subgroup Size, enter the subgroup size if it is constant (Optional, Integer, >=2) \n• In Lower Specification Limit, enter the lower specification limit (At least one limit is required, Numeric)\n• In Upper Specification Limit, enter the lower specification limit (At least one limit is required, Numeric)\n• In Historical Mean, enter the population proportion, otherwise it will be estimated from the sample (Optional, Numeric) \n• In Historical Sigma (Within), enter the within-subgroup sigma, population standard deviation or estimates from historical data, otherwise it will be estimated from the data (Optional, Numeric, >0)\n• In Historical Sigma (Between), enter the between-subgroup sigma, population standard deviation or estimates from historical data, otherwise it will be estimated from the data (Optional, Numeric, >0)\n• In Target, enter the target value. It is used to calculate Cpm (Optional, Numeric) \n• In Sigma Tolerance, enter the interval (number of standard deviations) to calculate the capability statistics, otherwise 6 standard deviations will be used (Numeric, >0) \n• In Method (Subgroup>1), choose the method of estimating sigma when subgroup size is greater than 1 \n• In Method (Subgroup=1), choose the method of estimating sigma when subgroup size is equals to 1\n• In Moving Range Length, enter the number of observations used to calculate the moving range (Integer, >=2)\n• In Display Capabilities in, choose the method to display capability indices\n• In Display Performance in, choose the method to display performance indices\n• Click OK"]
[null,"Example","You work in manufacturing plant and you need to make sure that the diameter of the parts made is 300mm ± 3mm to meet technical specifications. You collected five samples each day for the last 30 days. You want to perform a capability study to evaluate if the process is capable of meeting the specifications.\n• Open data worksheet by choosing ProcessMA > Tools > Data\n• Choose ProcessMA > Quality Tools > Capability Analysis > Capability Analysis (Between/Within) \n• In Variable, select D - Diameter \n• In Constant Subgroup Size, enter 10\n• In Lower Specification Limit, enter 298 \n• In Upper Specification Limit, enter 302\n• In Target, enter 300\n• Click OK"]
[null,"Results","The process does not meet the lower and upper specification limits. The process needs to be improved to reduce variation and also centered on the target."]
["Capability Analysis (Weibull)","Title","The Capability Analysis (Weibull) generates a process capability report containing various capability indices (Pp, Ppk, PPU, and PPL)."]
[null,"Details","It is used when the data is from a Weibull distribution. This procedure also generates a histogram of the data with a Weibull curve. ProcessMA uses maximum likelihood estimates for distribution parameters.\n\nInterpret Capability Indices\n• Pp measures the overall process capability, sometimes also referred to as long term performance. Therefore, if there are special cause variation present in the process data, Pp will be smaller than Cp.  \n• Ppk also measures the overall process capability but unlike Pp, it also take into consideration the location of the process mean in relation to the specification limits. Similar to the interpretation for Cp and Cpk, If the process is stable but off-target, Ppk will be smaller than Pp. \n• Z is an alternative measure of process capability. In simple terms, Z represents the number of standard deviations between the mean and the specification limit. For 2-sided specification limits, overall Z is smaller than the Z of each specification limit. \n• Observed Performance  The number process output that actually fail the specification limits based on your data. This metric can be expressed in terms of parts per million (PPM) or in percent. \n• Expected Performance  The number of process output that you expect to fail specification limits. This level of performance is what you customer will likely experience. This expectation is based on the distribution (using cumulative distribution function) used to model your data. The expected performance can be expressed in terms of parts per million (PPM) or in percent. "]
[null,"How to","Choose ProcessMA > Quality Tools > Capability Analysis > Capability Analysis (Weibull)\n\nIn Variable, select the column containing the data (Numeric) \n\nIn Lower Specification Limit, enter the lower specification limit (At least one limit is required, Numeric)\n\nIn Upper Specification Limit, enter the lower specification limit (At least one limit is required, Numeric)\n\nIn Historical Shape, enter the historical shape parameter value (Optional, Numeric, >0) \n\nIn Target, enter the target value. It is used to calculate Cpm (Optional, Numeric) \n\nIn Sigma Tolerance, enter the interval (number of standard deviations) to calculate the capability statistics, otherwise 6 standard deviations will be used (Numeric, >0) \n\nIn Display Capabilities in, choose the method to display capability indices\n\nIn Display Performance in, choose the method to display performance indices\n\nClick OK\n\n "]
[null,"Example","You are an engineer and you need to ensure the electrical stability of circuit boards. You recorded the length of time the circuit boards were unstable while being plugged in for a period of 30 days. You want to run a capability cnalysis based on the Weibull distribution.\n• Open data worksheet by choosing ProcessMA > Tools > Data\n• Choose ProcessMA > Quality Tools > Capability Analysis > Capability Analysis (Weibull)\n• In Variable, select AD - Unstable \n• In Upper Specification Limit, enter 3 "]
["Capability Analysis (Binomial)","Title","Capability Analysis (Binomial) generates process capability report for attribute data that follows the Binomial distribution"]
[null,"Details","The report includes a \n• P Chart to verify if the process is in statistical control\n• Cumulative %Defective chart to verify if the data have a consistent estimate of %defectives\n• Histogram of %Defective to help visualize the distribution of %defective of the sample data\n• Defective Rate Chart to verify that the %defective is not affected by the sample size \n• Binomial Plot (when subgroup size is constant) to verify that the expected %defectives are not affected by the observed %defectives \nThe most common types of Binomial data are records of defective output or Yes/No data. In order the use Capability Analysis (Binomial), you need to ensure that the following assumptions are valid:\n• The outcome is binary or have only 2 possible result\n• The probability of success is the same for all units \n• The outcome of each unit is independent of each other "]
[null,"How to","• Choose ProcessMA > Quality Tools > Capability Analysis > Capability Analysis (Binomial)\n• In Defectives, select the column containing the data (Integer, >=0) \n• In Sample Sizes, select the column containing sample sizes (Integer, >Defectives) \n• In Constant Sample Size, enter the sample size if it is constant (Optional, Integer, >Defectives) \n• In Historical P, enter the historical proportion of defectives(Optional, Numeric, >0 & <1) \n• In Target Defective, enter the defective target (Optional, Numeric, >0 & <1) \n• Click OK"]
[null,"Example","You are working in a software company and you want to assess the responsiveness of the customer support service. You recorded the number of enquiries received and the number of enquiries unresolved after 2 days, for the last 30 days.\n• Open data worksheet by choosing ProcessMA > Tools > Data\n• Choose ProcessMA > Quality Tools > Capability Analysis > Capability Analysis (Binomial)\n• In Defectives, select AE - Unresolved\n• In Sample Sizes, select AF - Enquiries \n• Click OK"]
[null,"Results","The P Chart shows that the process is in control.  The Cumulative % Defective shows the overall defectives settles at 12.4%.  The rate of defectives seems to increase with sample size.  The process Z is only 1.15, which means that the process needs much improvement."]
["Capability Analysis (Poisson)","Title","Capability Analysis (Poisson) generates process capability report for attribute data that follows the Poisson distribution."]
[null,"Details","The report includes a \n• U Chart to verify if the process is in statistical control\n• Cumulative mean DPU chart to verify if the data have a consistent estimate of mean \n• Histogram of DPU to help visualize the distribution of DPU of the sample data\n• Defect Rate Chart to verify that the DPU is not affected by the sample size \n• Poisson Plot (when subgroup size is constant) to verify that the expected number of defects are not affected by the observed number of defects\n• The most common types of Poisson data are records of defects per unit. In order the use Capability Analysis (Poisson), you need to ensure that the following assumptions are valid:\n• The rate of defects is the same for each unit \n• The number of defects in each unit is independent of each other "]
[null,"How to","• Choose ProcessMA > Quality Tools > Capability Analysis > Capability Analysis (Poisson)\n• In Defects, select the column containing the data (Integer, >=0) \n• In Sample Sizes, select the column containing sample sizes (Integer, >Defectives) \n• In Constant Sample Size, enter the sample size if it is constant (Optional, Integer, >Defectives) \n• In Historical Mean , enter the population mean (Optional, Numeric) \n• In Target DPU, enter the target DPU value (Optional, Numeric) \n• Click OK"]
[null,"Example","You work in a refrigerator manufacturing plant. You need to ensure that the surface of the refrigerators is in good condition. You inspect a random surface area of 100cm2 of each refrigerator and recorded the number of scratches and dents found.\n• Open data worksheet by choosing ProcessMA > Tools > Data\n• Choose ProcessMA > Quality Tools > Capability Analysis > Capability Analysis (Poisson)\n• In Defects, select AG - Scratches \n• In Constant Sample Size, enter 100\n• Click OK"]
[null,"Results","The U Chart shows that there are several points out of control. The Cumulative DPU chart shows that the overall DPU settles at 0.023."]
["Sigma Calculator","Title","This procedure provides a simple calculation for sigma level and other common performance measurements."]
[null,"How to","• Choose ProcessMA > Quality Tools > Sigma Calculator \n• For Basic Calculator, enter number of opportunities and number of defects to compute the results. \n• For Advanced Calculator, enter the number of units sampled, number of opportunities per unit, number of defects (total), known sigma shift (default 1.5) to compute the results."]
[null,"Example","Your factory produces 4000 capacitors a day and of which 23 are defective. Calculate the sigma performance.\n• Choose ProcessMA > Tools > Load Examples\n• In Category, select Capability Analysis \n• In Tool, select Sigma Calculator "]
["GAGE R&R"]
["Gage Run Chart","Title","The Gage Run Chart plots the measurements by operator and by part, and a reference line at the overall mean."]
[null,"Details","It is used to visualise measurement between different operators and parts. If there are multiple trials, only the first 10 trials will be plotted. "]
[null,"How to","• Choose ProcessMA > Quality Tools > Gage R and R > Gage Run Chart \n• In Measurement, select the column containing measurement data (Numeric) \n• In Part, select the column containing part indicators (>=2 distinct values) \n• In Operator, select the column containing operator indicators\n• In Trial, select the column containing trial numbers\n• In Historical Mean, enter a value for the reference line, else the mean of the measurements will be used \n• Click OK"]
[null,"Example","You collected measurements made by 3 different operators on 10 different parts. You want to use the Gage Run Chart to assess the measurement differences between operators and parts.\n• Open data worksheet by choosing ProcessMA > Tools > Data\n• Choose ProcessMA > Quality Tools > Gage R and R > Gage Run Chart \n• In Measurement, select AQ - Measurement \n• In Part, select AR - Part \n• In Operator, select AS - Operator \n• Click OK"]
[null,"Results","From the chart, it seems that most of the variation is due to differences between parts. It also appears that Operator 1 is relatively inconsistent and Operator 2’s second measurement is frequently smaller than the first measurement."]
["Gage Linearity and Bias Study","Title","The Gage Linearity and Bias Study can be used to determine the accuracy of your measurements through the expected measurement range."]
[null,"Details","In other words, it can help you determine if your gage has the same accuracy when measuring objects of different sizes and if your gage is biased when compared to a master value."]
[null,"How to","• Choose ProcessMA > Quality Tools > Gage R and R > Gage Linearity and Bias Study \n• In Measurement, select the column containing measurement data (Numeric) \n• In Part, select the column containing part indicators (>=2 distinct values) \n• In Reference, select the column containing master measurements (Numeric) \n• In Process Variation , enter a value for the process standard deviation (Optional, Numeric, >0) \n• Click OK"]
[null,"Example","You want to determine the accuracy of the measurement gage in your plant. You selected five parts to study which represented the range of measurements that you need to take. You also have the master value for each of these five parts. You got an operator to measure the parts in random and 10 times each.\n• Open data worksheet by choosing ProcessMA > Tools > Data\n• Choose ProcessMA > Quality Tools > Gage R and R > Gage Linearity and Bias Study \n• In Measurement, select AT - Readings\n• In Part, select AU - Samples \n• In Reference, select AV - Reference \n• Click OK"]
[null,"Results","The gage linearity and gage bias account for 1.3% and 5.8% of the overall process variation respectively."]
["Gage R&R","Title","The Gage Repeatability and Reproducibility study helps you to determine how much of the observed process variation is due to measurement system variation."]
[null,"Details","It breaks down the overall variation into variation due to part-to-part, repeatability and reproducibility. The ANOVA method is commonly used as it also breaks fown reproducibility into operator and operator by part interactions. This tool can be used on crossed Gage R&R studies at which each part is measured by each operator several times. The following are some guidances to set up a Gage R&R study.\n• Parts measured should cover the entire range of possible values to get a better estimate of part-to-part variation\n• If you can run limited number of tests, it is better to test more parts than take more measurements on the same part to get a better chance of detecting linearity issues\n• Ensure complete randomization of the measurement process. Repeating measurement of the same part by the same operator too often may produce over-optimistic estimates. \n• If the variation among operators for the same part is large, you may need more operators to get a better estimate of reproducibility"]
[null,"How to","• Choose ProcessMA > Quality Tools > Gage R and R > Gage R and R\n• In Measurement, select the column containing measurement data (Numeric) \n• In Part, select the column containing part indicators (>=2 distinct values) \n• In Operator, select the column containing operator indicators\n• In Method of Analysis, choose the method to use for analysis. The Xbar and R method distinguishes the observed process variation into part-to-part, repeatability and reproducibility components. The ANOVA method is similar but it also breaks down reproducibility into operator and operator by part components\n• In Study Variation, enter a value to be used to calculate Study Variation. The default is 6, which is the number of standard deviations needed to capture 99.73% of your process measurements (Optional, Numeric, >0) \n• In Process Tolerance, enter the tolerance range (USL - LSL) if known (Optional, Numeric) \n• Click OK"]
[null,"Example","Three operators took measurements on 10 parts, twice on each part. You want to determine how much of the observed process variation is due to measurement system variation.\n• Open data worksheet by choosing ProcessMA > Tools > Data\n• Choose ProcessMA > Quality Tools > Gage R and R > Gage R and R\n• In Measurement, select AQ - Measurement \n• In Part, select AR - Part \n• In Operator, select AS - Operator \n• Click OK"]
[null,"Results","By looking at %VarComp, the variation due to differences between parts (Part-to-Part) contributes 94.1% to the overall variation. It is much larger than that of the Total Gage R&R at 5.9%. The same observation can be made by looking at the Component of Variation Chart. This indicates that measurement system error is small. From the By Part Chart, the variation of the red line shows that there are significant differences between parts. On the other hand, from the By Operator Chart, the red line is relatively flat, which indicates that the differences between operators are small. In addition, most of the points in the Xbar Chart for Measurement by Operator are out-of-control, indicating that variation is mainly due to differences between parts."]
["Attribute Gage Study","Title","The Attribute Gage Study examines the precision of a measurement system when measurement is binary."]
[null,"Details","It calculates the amount of bias and repeatability of the measurement system. This study only give indicative information on whether a part is good or bad based on a set of predefined standard. To use this tool, you need to select parts of different values and you should know the standard value of each part. If you are using the AIAG method, you must at exactly 20 trials per part. If you are using the regression method, the minimum is 15 trials per part. However, to obtain good estimates of bias and repeatability, 20 trials per part is recommended. Addition requirements are as follows:\n• Data collected for at least eight different parts \n• Smallest part are all bad\n• Largest part are all good\n• For AIAG method, exactly six parts have a mixture of good and bad units. For regresion method, more than six parts are allowed \n• If a lower tolerance limit is specified, the part with the smallest standard value are all bad and the part with the largest standard value are all good. Also the number of good parts should increase as the standard value increases\n• If a upper tolerance limit is specified, the opposite must be specified "]
[null,"How to","• Choose ProcessMA > Quality Tools > Gage R and R > Attribute Gage Study \n• In Part, select the column containing part indicators (>=2 distinct values) \n• In Reference, select the column containing reference values or known standards (Numeric) \n• In Acceptance, select the column containing number of accepted trials (Integer, >=0)\n• In Trial, select the column containing number of trials (Integer, >0)\n• In Constant No. of Trial, enter the number of trials if it is constant (Integer, >0) \n• In Tolerance Limit to Use, choose if you want to use the lower limit or upper limit\n• In Tolerance Limit, enter a value for the tolerance level (Numeric)\n• In Method, choose the method use to test the bias of the gage\n• Click OK"]
[null,"Example","You want to determine the bias and repeatability of an attribute (pass/fail) measurement system. You measured 10 parts of different reference values, 15 times each. You know that the system has a lower tolerance of 0.2 and an upper tolerance of 1.0.\n• Open data worksheet by choosing ProcessMA > Tools > Data\n• Choose ProcessMA > Quality Tools > Gage R and R > Attribute Gage Study \n• In Part, select AW - Part_Att\n• In Reference, select AX - Reference_Att\n• In Acceptance, select AY - Acceptance_Att\n• In Constant No. of Trial, enter 20 \n• In Tolerance Limit, enter 0.2 \n• Click OK"]
[null,"Results","The bias and repeatability is shown in the output. The p-value for the test for bias is 0, suggesting that bias is present in the measurement system."]
["Attribute Agreement Analysis","Title","The Attribute Agreement Analysis is used to assess the accuracy of subjective ratings (with or without natural ordering) by operators."]
[null,"Details","In general, it is more likely that subjective ratings are accurate and useful if there is substantial agreement in measurements among appraisers. Examples of subjective rating are such as taste of coffee, quality of colouring, etc. "]
[null,"How to","• Choose ProcessMA > Quality Tools > Attribute Agreement Analysis \n• In Rating, select the column containing rating data\n• In Sample, select the column containing sample indicators\n• In Appraiser, select the column containing appraiser indicators\n• In Standard, select the column containing known standard or master value for each sample (Numeric) \n• Check Attribute Data is Ordered, if your measurement data have more than two levels and are ordinal\n• Check Show Kappa and Kendall, if you want to display the kappa coefficient tables and Kendall's coefficient tables\n• Click OK"]
[null,"Example","You work in a garment factory and you have just trained 4 new quality controllers. The quality controllers need to determine is the garments are ‘up-to-standard’. You want to assess if these new quality controllers are ready for the job. You asked each quality controller to give their ratings on 10 garments on a five-point scale (-2, -1, 0, 1, 2).\n• Open data worksheet by choosing ProcessMA > Tools > Data\n• Choose ProcessMA > Quality Tools > Attribute Agreement Analysis \n• In Rating, select AZ - Rating \n• In Sample, select BA - Garment \n• In Appraiser, select BB - Controller \n• In Standard, select BC - Standard \n• Check Attribute Data is Ordered\n• Check Show Kappa and Kendall\n• Click OK"]
[null,"Results","The Each Appraiser VS Standard assessment agreement table shows that Frances was only able to matched 5 out of the 10 assessments while Mary was able to match all of them. The confidence interval of %Matched is shown in the table and also plotted as a chart. Based on this study, you conclude than Frances is in most need of more training."]
["Mapping"]
["Mind Mapping","Title","The Mind Mapping tool is interactive and can be used to draw relational maps."]
[null,"Details","Use it to draw mind maps, CTQ tree, drivers map, cause and effect diagram such as fishbone and 5 whys or even organisation charts."]
[null,"How to","• Choose ProcessMA > Quality Tools > Mind Mapping\n• A new mind mapping worksheet will be created with one Parent node \n• To add a child node, enter text in the cell below the node (parent)\n• To delete a node (and all its child nodes), enter '#' in the cell below the node you want to delete\n• To change the text of a node, enter '\\' followed by the new text\n\nMind Mapping - Fishbone and Mind Mapping - 5 Whys are similar in nature and the only difference is that they have pre-populated nodes. "]
["Process Mapping","Title","The Process Mapping tool helps you draw diagrams like process maps, value stream maps, etc. "]
[null,"Details","You can type directly in the drawing worksheet and let ProcessMA draw automatically for you or you can draw using the Toolbar."]
[null,"How to","• Choose ProcessMA > Quality Tools > Process Mapping > New \n\nMethod 1: Create a process map using the toolbar\n• To launch the toolbar, choose ProcessMA > Quality Tools > Process Mapping > Toolbar\n• To draw symbols, click on the appropriate symbol (SB) buttons\n• To view more symbols, click on the tabs on the top of the toolbar\n• To add colours to an existing symbol, select the symbol first (by clicking on the outline of the shape) and click on the appropriate colour buttons \n• To draw connectors, click on the appropriate connector buttons and click on the connection points of any existing symbols you wish to connect\n• To enable option to snap (align) symbols drawn to the gridlines on the worksheet, click on the snap-to-grid button\n \nMethod 2: Draw as you type\n• To draw a standard symbol, type anywhere on the worksheet and let ProcessMA draw automatically\n• To draw-as-you-type, select On in Cell I1. Conversely, to disable draw-as-you-type, select Off in Cell I1\n• You can also specify the size of the symbol drawn. Enter the number of grid intervals you want to set for the the height and width in Cell I2 and Cell I3 respectively\n• To draw multiple symbols at once, copy / paste a list of words onto the process mapping worksheet\n• To draw specific symbols, type the appropriate prefix followed by '>' and the text you wish to insert into the symbol. The prefixes are displayed in the toolbar. Example, if you type 'pd>Approve case', a Pre-defined symbol will be drawn with the entered text embedded \n• You can also draw specific symbols by typing keywords. For example, if you type \"Create document\", a Document symbol will be drawn with the entered text embedded. The word 'document' is a listed keyword for the Document symbol. You can customize your own keywords using the toolbar. Remember to click the Save button to store your changes. To restore keywords to original settings, click the Default button. To exit without saving, click the Close button. \n• Draw a connecting symbol: Type in the nearby cells of an existing symbol to draw a connected new symbol\n• Change existing symbol: Type the appropriate prefix in the cells below an existing symbol to change it to a new symbol"]
["Gantt Chart","Title","The worksheet helps you to draw a Gantt chart. A Gantt chart is useful for project planning and monitoring."]
[null,"How to","• Choose ProcessMA > Quality Tools > Gantt Chart > New \n\nSetting up the Gantt Chart for your project: \n• Enter the overall start date of project in Cell C1\n• Select the calendar interval in Cell D1\n• Select the definition of non-working days in Cell E1 \n\nCreate a task:\n• In ID, enter the serial number of the task\n• In Task, enter a description of the task\n• In Start Date, enter the date the task begins\n• In End Date, enter the date the task ends\n• In Duration, enter the number of days the task will take\n• In Completion, enter how much the task has been completed, in percent\n• In Milestone, enter ‘Yes’ if the task is a milestone. Otherwise, leave it blank\n• In Remarks, enter miscellaneous information about the task\n• In Predecessor, enter the ID of the task which must be completed before this task can begin. To Multiple entries must be separated by commas (,) \n\nDraw timeline on the chart directly : \nInstead of entering the start and end date of each task in Column C:D, you can alternatively specify the timeline directly on the Gantt chart. To do so, type 'S' in the appropriate cell to indicate the start of the task and type 'E' in the appropriate cell to indicate the end of the task. The timeline will automatically be drawn on the Gantt chart and the start and end date updated automatically."]
[null,"How to","Updating the Gantt chart\nThe Gantt chart needs to be updated manually by choosing ProcessMA > Quality Tools > Gantt Chart > Update in the following scenarios:\n• Changes in predecessor\n• Changes in master and sub tasks\n• Update multiple task at once (E.g. copy and paste details of multiple tasks onto Gantt Chart)\n\nCreate a subtask:\nYou can create master task and sub task by manipulating the task IDs. The method is similar to standard numbering system. For example, task IDs ‘1.1’, ‘1.2’, ‘1.3’ are sub tasks to task ID ‘1’. Similarly, task ID ‘1.1.1’, ‘1.1.2’, ‘1.1.3’ are sub tasks to task ID ‘1.1’. Note that tasks must be arranged together and in ascending order. Note: You may need to manually update the Gantt chart by choosing ProcessMA > Quality Tools > Gantt Chart > Update \n\nDetermine slack and conflict:\nIf you have predecessor task in your project, you need to update your Gantt chart to determine the slack and conflict. If there is any slack or conflict for any task, it will be displayed in 'Log' For example:\n• 'S – 10': This task has a predecessor task which must be completed before it can start. However, there is a slack of 10 days from the end of the predecessor task and its start. Therefore, you can consider to let this task start 10 days earlier.\n• 'C– 5': This task has a predecessor task which must be completed before it can start. However, this task is planned to start 5 days before its predecessor is completed. Therefore, you need to postpone this task by 5 days to resolve the conflict.\n• 'U': This task is a master task and there is a mismatch between its timeline and its sub tasks’ timeline. The conflict may arise if any sub tasks has an earlier start date or a later end date than their master task."]
["Templates","Title","ProcessMA provides a list of useful templates to aid you in various stages of your project and planning process."]
[null,"Details","Some of these templates can be customized to user requirements. "]
[null,"How to","• Choose ProcessMA > Quality Tools > Template and select the template you want to create\n• For C&E Matrix and Pugh Matrix, enter the number of columns and number of rows to form the matrix and click OK \n• For Pair-wise Comparison, enter the number of factors to compare and click OK\n• For QFD, enter the number of columns and number of rows to form the matrix, select the relevant sections to display and click OK\n• For the remaining template, a blank template will be created automatically"]
["GRAPH"]
["Run Chart","Title","The Run Chart plots individual observations in run order and is used to identify common cause and special cause variations."]
[null,"Details","It can also perform tests for trends, oscillation, mixtures and clustering (special causes or non-random behaviors)."]
[null,"How to","• Choose ProcessMA > Graphs > Run Chart \n• In Variable, select the column containing the data (Numeric) \n• Check Plot Mean, if you want to plot mean line\n• Click OK"]
[null,"Example","You are the quality control engineer in an electronic manufacturing plant. You need to ensure that the switches manufactured are durable. You collected data from the testing laboratory on the number of times the switches are used before breaking down. You want to generate a Run Chart to study the variation.\n• Open data worksheet by choosing ProcessMA > Tools > Data\n• Choose ProcessMA > Graphs > Run Chart \n• In Variable, select E - Switches \n• Check Plot Mean\n• Click OK"]
[null,"Results","The P-value for clustering is 0.033. If the desired level of significance is 0.05, it suggests that there are special causes in the process."]
["Pareto Chart","Title","The Pareto Chart is a type of bar charts where bars are categories and the height of the bar represents its frequency."]
[null,"Details","The bars are sequenced in descending order and there is also a cumulative percentage line that indicates the added contribution of each category to the total. The Pareto Chart is usually used to identify the ‘vital few’ from the ‘trivial many’. For example, if categories are different types of defects, it helps you identify the most frequently occurring defect to help you focus improvement efforts."]
[null,"How to","• Choose ProcessMA > Graphs > Pareto Chart\n• In Variable, select the column containing the data (Numeric) \n• In Frequency, select the column containing frequency counts (Optional, Integer) \n• In % To Comine, enter value to combine categories with percent contribute less than or equals to it (Optional, Numeric, >0, <1) \n• Click OK"]
[null,"Example","You found out that one of the reasons for processing delays is due to incomplete application forms. You collected data on the type of information missing in the application forms received for the past 2 weeks. You want to use the Pareto Chart to identify the types of information that are most frequently missing.\n• Open data worksheet by choosing ProcessMA > Tools > Data\n• Choose ProcessMA > Graphs > Pareto Chart\n• In Variable, select A - Missing \n• Click OK"]
[null,"Results","Since 76% of the missing information in application forms are ‘bank code’ and ‘invoice number’, you may want to focus improvement efforts on resolving these two issues first."]
["Multi-Vari Chart","Title","The Multi-Vari chart is used to display ANOVA data for up to 4 factors."]
[null,"Details","It is commonly used as a preliminary analysis of the data to assess the means for each factor level. Each factor should have at least 2 distinct levels."]
[null,"How to","• Choose ProcessMA > Graphs > Multi-Vari Chart \n• In Variable, select the column containing the response data (Numeric) \n• In Factor 1 , select the column containing factor levels of the first factor (>=2 distinct values) \n• In Factor 2 , select the column containing factor levels of the second factor (Optional, >=2 distinct values) \n• In Factor 3 , select the column containing factor levels of the third factor (Optional, >=2 distinct values) \n• In Factor 4 , select the column containing factor levels of the fourth factor (Optional, >=2 distinct values) \n• Click OK"]
[null,"Example","You conducted an experiment to study how well organisms multiple in different temperatures and in the presence of different catalysts. You prepared 18 dishes of organisms and placed them at three different temperatures and added three different types of catalyst. You recorded the number of organism in each dish after 10 days. You want to visualise the data to see if there are any trends and interactions.\n• Open data worksheet by choosing ProcessMA > Tools > Data\n• Choose ProcessMA > Graphs > Multi-Vari Chart \n• In Variable, select L - Organism \n• In Factor 1 , select M - Temperature \n• In Factor 2 , select N - Catalyst\n• Click OK"]
["Histogram","Title","The Histogram is a type of bar charts where bars are intervals of continuous data and the height of the bars represent the frequency for that interval."]
[null,"Details","It can also plot a fitted probability density function that can be used to assess how well the data follows a normal distribution. The Histogram can be used to visualise the distribution of the data."]
[null,"How to","• Choose ProcessMA > Graphs > Histogram\n• In Variable, select the column containing the data (Numeric) \n• In Interval, select the column containing user specified interval classes (Optional, Numeric) \n• Check Plot Normal Curve, if you want to plot normal curve in the histogram\n• Click OK"]
[null,"Example","You work in manufacturing plant and you need to make sure that the diameter of the parts manufactured is 300mm ± 3mm to meet technical specifications. You want to generate a histogram to visualise the distribution.\n• Open data worksheet by choosing ProcessMA > Tools > Data\n• Choose ProcessMA > Graphs > Histogram\n• In Variable, select D - Diameter \n• Check Plot Normal Curve\n• Click OK"]
["Pie Chart","Title","The Pie Chart can be used to visualise the contribution of various categories to the whole."]
[null,"How to","• Choose ProcessMA > Graphs > Pie Chart \n• In Variable, select the column containing the data (Numeric) \n• In Frequency, select the column containing frequency counts (Optional, Integer) \n• In % To Comine, enter value to combine categories with percent contribute less than or equals to it (Optional, Numeric, >0, <1) \n• Click OK"]
[null,"Example","You are the sales manager and you have collected past 3 months data on the sales made by various account managers. You want to use the Pie Chart to visualise the contribution to sales by the various account managers working for you.\n• Open data worksheet by choosing ProcessMA > Tools > Data\n• Choose ProcessMA > Graphs > Pie Chart \n• In Variable, select F - Account Manager \n• Click OK"]
["Time Series Plot","Title","The Time Series Plot plots observations in the order of time."]
[null,"How to","• Choose ProcessMA > Graphs > Time-Series Plot \n• In Variable, select the column containing the data (Numeric) \n• In Time Stamp, select the column containing time stamp data (Date)\n• Click OK"]
[null,"Example","You gathered sales data for the last 24 months. You want to use the Time Series Plot to see the performance for the past 24 months.\n• Open data worksheet by choosing ProcessMA > Tools > Data\n• Choose ProcessMA > Graphs > Time-Series Plot \n• In Variable, select Q - Revenue\n• In Time Stamp, select R - Month\n• Click OK"]
["Scatter Plot","Title","The Scatter Plot plots observations based on its x and y coordinates."]
[null,"How to","• Choose ProcessMA > Graphs > Scatter Plot \n• In Variable (Y), select the column containing y variable data (Numeric) \n• In Variable (X), select the column containing x variable data (Numeric) \n• Click OK"]
[null,"Example","You want to model the relationship between the size of the valve and the speed of the machine. You collected data on various settings of the valve size and the resultant speed of the machine. You want to visualise the relationship in a Scatter Plot.\n• Open data worksheet by choosing ProcessMA > Tools > Data\n• Choose ProcessMA > Graphs > Scatter Plot \n• In Variable (Y) , select O - Speed \n• In Variable (X) , select P - Valve \n• Click OK"]
["Dotplot","Title","The Dotplot is similar to the histogram but frequency is represented by the number of dots."]
[null,"Details","A dot represents one observation or a group of observations if they are of the same or about the same value. The dots are plotted along the x-axis which are divided into intervals and dots are stacked vertically if there is more than one in the same interval. The Dotplot is useful for comparing and assessing distributions."]
[null,"How to","• Choose ProcessMA > Graphs > Dotplot\n\nFor data in single stacked column \n• In Variable, select the column containing the data (Numeric) \n• In Subgroup, select the column containing subgroup indicators (Optional)\n\nFor data in different columns \n• In Variables, select the columns containing the response data (Numeric, >= 2 variables)\n• Click OK "]
[null,"Example","A company makes steel bolts using four different machines. You want to assess if the dimensions of the steel bolts made by different machines are the same. You want to use the Dotplot to compare the distributions.\n• Open data worksheet by choosing ProcessMA > Tools > Data\n• Choose ProcessMA > Graphs > Dotplot\n• In Variable, select B - Dimension \n• In Subgroup, select C - Machine\n• Click OK "]
["Boxplot","Title","The boxplot (also called the box-and-whisker plot) represents the distribution of data as a box and whiskers."]
[null,"Details","It is useful for comparing the distribution of various groups of data.\n• Outlier - Unusually small or large observation\n• Upper control - Upper limit which is = Q3 + 1.5 (Q3 - Q1)\n• Q3 - Third quartile, where 75% of the data are less than or equals to this value\n• Q2 - Median, where 50% of the data are less than or equals to this value \n• Q1 - First quartile, where 25% of the data are less than or equals to this value\n• Lower control - Lower limit which is = Q1 - 1.5 (Q3 - Q1)"]
[null,"How to","• Choose ProcessMA > Graphs > Boxplot\n\nFor data in single stacked column \n• In Variable, select the column containing the data (Numeric) \n• In Subgroup, select the column containing subgroup indicators (Optional) \n\nFor data in different columns \n• In Variables, select the columns containing the response data (Numeric, >= 2 variables)\n• Check Show Outliers, if you want to plot outliers, which are represented as *\n• Check Show Median Label, if you want to show median values\n• Check Show Mean Label, if you want plot and show mean values \n• Click OK"]
[null,"Example","A company makes steel bolts using four different machines. You want to assess if the dimensions of the steel bolts made by different machines are the same. You want to use Boxplot to compare the distributions.\n• Open data worksheet by choosing ProcessMA > Tools > Data\n• Choose ProcessMA > Graphs > Boxplot\n• In Variable, select B - Dimension \n• In Subgroup, select C - Machine \n• Check Show Outliers\n• Check Show Median Label\n• Check Show Mean Label\n• Click OK"]
["Matrix Plot","Title","The Matrix Plot is made up of individual scatter plots for several variables."]
[null,"Details","It is useful for visualising the relationship among many variables, pairwise, all in the same chart. Note: Limited to 10 variables at one time."]
[null,"How to","• Choose ProcessMA > Graphs > Matrix Plot \n• In Variables, select the columns containing the data (Numeric, >=2 Variables) \n• Check Plot Partial, if you want to plot lower half the matrix plot only\n• Click OK"]
[null,"Example","You know that sales revenue is dependent on the number of sales representatives on the field, the amount spent on marketing and the range of products offered. You gathered data from 30 branches and you want to visualise the relationship between sales revenue and its factors.\n• Open data worksheet by choosing ProcessMA > Tools > Data\n• Choose ProcessMA > Graphs > Matrix Plot\n• In Variables, select G - Sales, H - Reps, I - Marketing, J - Products \n• Check Plot Partial\n• Click OK"]
["Probability Plot","Title","This can be used to display a probability plot for variables."]
[null,"How to","• Choose ProcessMA > Graphs > Probability Plot \n• In Variable, select the column containing the data (Numeric) \n• In Distribution, choose the distribution to fit \n• In Confidence Level, enter the desired confidence level (Numeric, >0 & <1)\n• Check Show Confidence Interval, if you want to display confidence interval in the probability plot\n• Enter the know historical parameters for the respective distribution is required (Optional, Numeric) \n• Click OK"]
[null,"Example","You work in a manufacturing plant making widgets and you collected failure times for 50 widgets. You want to determine if a Normal distribution fits your data.\n• Open data worksheet by choosing ProcessMA > Tools > Data\n• In Variable, select CD - Failure Times \n• In Distribution, choose Normal \n• Check Show Confidence Interval\n• Click OK"]
[null,"Results","The data fits a normal distribution with mean of 161.6 and standard deviation of 21.527 fairly well."]
["RELIABILITY AND SURVIVAL"]
["Parametric Dist Analysis (Right)","Title","This tool performs Parametric Distribution Analysis for uncensored and right censored data."]
[null,"Details","It can be used to determine an appropriate distribution to fit your data by assessing how closely the plot points fit the cumulative density function. You can also use the Anderson-Darling or Pearson correlation coefficient to assess the goodness-of-fit. In addition, you can estimate percentiles and survival probabilities and visualise your data in survival, cumulative failure and hazard plots."]
[null,"How to","• Choose ProcessMA > Reliability and Survival > Distribution Analysis (Right Censoring) > Parametric Distribution Analysis \n• In Variable, select the column containing the data (Numeric) \n• In Frequency, select the column containing frequency counts (Optional, Positive integer) \n• In Assumed Distribution, choose the distribution to fit \n• Under Censor Tab, in Censor, select the column containing censoring indicator (Optional, Exactly 2 distinct values - censored and uncensored) \n• Under Censor Tab, in Censor Value, choose the indicator you use to indicate censoring\n• Under Estimate Tab, in Estimation Method, choose the method used to estimate distribution parameters\n• Under Estimate Tab, in Method, choose the method used to estimate plot points\n• Under Estimate Tab, in Set Shape/Scale At, enter a known shape and scale parameter for the variable (Optional, Numeric) \n• Under Result Tab, check Show Parameter Estimates, if you want to estimate distribution parameters \n• Under Result Tab, check Show Characteristics, if you want to calculate distribution characteristics\n• Under Result Tab, check Estimate Percentiles, if you want to calculate percentile values for specific percent\n• Under Result Tab, in Percent, enter the percent values you want to calculate percentiles (Optional, Numeric, >0 & <100, Separate multiple entries with commas)\n• Under Result Tab, check Estimate Survival Probabilities, if you want to calculate survival probabilities for values for specific times \n• Under Result Tab, in Times, enter the time value you want to calculate survival probabilities (Optional, Numeric, >0, Separate multiple entries with commas)\n• Under Result Tab, in Confidence Level, enter the desired confidence level (Numeric, >0 & <1)\n• Under Graph Tab, check Probability Plot, if you want to display probability plot\n• Under Graph Tab, check Probability Density Plot, if you want to display probability density plot \n• Under Graph Tab, check Survival Plot, if you want to display survival plot\n• Under Graph Tab, check Cumulative Failure Plot, if you want to display cumulative failure plot\n• Under Graph Tab, check Hazard Plot, if you want to display hazard plot\n• Under Graph Tab, check Show Confidence Interval, if you want to display confidence interval in the above plots \n• Click OK"]
[null,"Example","You work in a manufacturing plant making widgets and you want to find out the time at which 5% of widgets will fail. You have collected failure times for 50 widgets but some widgets dropped out of the test. The failure times marked ‘F’ indicates actual failure times and ‘C’ indicates censored units. You want to find out the times at various percentages of widgets fail and the proportion of widgets that survive more than 150 months.\n• Open data worksheet by choosing ProcessMA > Tools > Data\n• Choose ProcessMA > Reliability and Survival > Distribution Analysis (Right Censoring) > Parametric Distribution Analysis \n• In Variable, select CD - Failure Times \n• In Assumed Distribution, choose Lognormal \n• Under Censor Tab, in Censor, select CE - Censor \n• Under Censor Tab, in Censor Value, choose C \n• Under Result Tab, check Show Parameter Estimates\n• Under Result Tab, check Show Characteristics\n• Under Result Tab, check Estimate Percentiles\n• Under Result Tab, check Estimate Survival Probabilities\n• Under Result Tab, in Times, enter 150 \n• Click OK"]
[null,"Results","From the table of percentiles, you can see that it takes 124.3363 months for 5% of the widgets to fail. From the table of survival probabilities, you can see that 70.34% survive more than 150 months."]
["Nonpara Dist Analysis (Right)","Title","If you have uncensored or right censored data and no distribution fits your data, the Nonparametric Distribution Analysis can be used to estimate cumulative failure probabilities, hazard rates and draw survival, cumulative failure and hazard plots."]
[null,"How to","• Choose ProcessMA > Reliability and Survival > Distribution Analysis (Right Censoring) > Nonparametric Distribution Analysis\n• In Variable, select the column containing the data (Numeric) \n• In Frequency, select the column containing frequency counts (Optional, Positive integer) \n• Under Censor Tab, in Censor, select the column containing censoring indicator (Optional, Exactly 2 distinct values - censored and uncensored) \n• Under Censor Tab, in Censor Value, choose the indicator you use to indicate censoring\n• Under Estimate Tab, in Confidence Level, enter the desired confidence level (Numeric, >0 & <1)\n• Under Graph Tab, check Survival Plot, if you want to display survival plot\n• Under Graph Tab, check Cumulative Failure Plot, if you want to display cumulative failure plot\n• Under Graph Tab, check Hazard Plot, if you want to display hazard plot\n• Under Graph Tab, check Show Confidence Interval, if you want to display confidence interval in the above plots \n• Click OK"]
[null,"Example","You work in a manufacturing plant making widgets and you want to find out the time at which 5% of widgets will fail. You have collected failure times for 50 widgets but some widgets dropped out of the test. The failure times marked ‘F’ indicates actual failure times and ‘c’ indicates censored units. You want to find out the time at which half the widgets fail.\n• Open data worksheet by choosing ProcessMA > Tools > Data\n• Choose ProcessMA > Reliability and Survival > Distribution Analysis (Right Censoring) > Nonparametric Distribution Analysis\n• In Variable, select CD - Failure Times \n• Under Censor Tab, in Censor, select CE - Censor \n• Under Censor Tab, in Censor Value, choose C \n• Click OK"]
[null,"Results","The estimated median failure time is 157 months."]
["Parametric Dist Analysis (Arbitrary)","Title","This tool performs Parametric Distribution Analysis for uncensored and arbitrarily censored data."]
[null,"Details","It can be used to determine an appropriate distribution to fit your data by assessing how closely the plot points fit the cumulative density function. You can also use the Anderson-Darling or Pearson correlation coefficient to assess the goodness-of-fit. In addition, you can estimate percentiles and survival probabilities and visualise your data in survival, cumulative failure and hazard plots."]
[null,"How to","• Choose ProcessMA > Reliability and Survival > Distribution Analysis (Arbitrary Censoring) > Parametric Distribution Analysis\n• In Start, select the column containing start times (Numeric, Use * to represent left-censored data) \n• In End, select the column containing end times (Numeric, Use * to represent right-censored data) \n• In Frequency, select the column containing frequency counts (Optional, Positive integer) \n• In Assumed Distribution, choose the distribution to fit \n• Under Estimate Tab, in Estimation Method, choose the method used to estimate distribution parameters\n• Under Estimate Tab, in Set Shape/Scale At, enter a known shape and scale parameter for the variable (Optional, Numeric) \n• Under Result Tab, check Show Parameter Estimates, if you want to estimate distribution parameters \n• Under Result Tab, check Show Characteristics, if you want to calculate distribution characteristics\n• Under Result Tab, check Estimate Percentiles, if you want to calculate percentile values for specific percent\n• Under Result Tab, in Percent, enter the percent values you want to calculate percentiles (Optional, Numeric, >0 & <100, Separate multiple entries with commas)\n• Under Result Tab, check Estimate Survival Probabilities, if you want to calculate survival probabilities for values for specific times \n• Under Result Tab, in Times, enter the time value you want to calculate survival probabilities (Optional, Numeric, >0, Separate multiple entries with commas)\n• Under Result Tab, in Confidence Level, enter the desired confidence level (Numeric, >0 & <1)\n• Under Graph Tab, check Probability Plot, if you want to display probability plot\n• Under Graph Tab, check Probability Density Plot, if you want to display probability density plot \n• Under Graph Tab, check Survival Plot, if you want to display survival plot\n• Under Graph Tab, check Cumulative Failure Plot, if you want to display cumulative failure plot\n• Under Graph Tab, check Hazard Plot, if you want to display hazard plot\n• Under Graph Tab, check Show Confidence Interval, if you want to display confidence interval in the above plots \n• Click OK"]
[null,"Example","You work in a manufacturing plant making widgets and you want to find out the times at which widgets will fail. You have inspected the widgets at regular times (every 100 hours) to see how many have failed. You want to find out the times at various percentages of widgets fail and the proportion of widgets that survive more than 450 hours.\n• Open data worksheet by choosing ProcessMA > Tools > Data\n• Choose ProcessMA > Reliability and Survival > Distribution Analysis (Arbitrary Censoring) > Parametric Distribution Analysis\n• In Start, select CF - Start \n• In End, select CG - End \n• In Frequency, select CH - Frequency \n• In Assumed Distribution, choose Smallest Extreme Value \n• Under Result Tab, check Show Parameter Estimates\n• Under Result Tab, check Show Characteristics\n• Under Result Tab, check Estimate Percentiles\n• Under Result Tab, check Estimate Survival Probabilities\n• Under Result Tab, in Times, enter 450 \n• Click OK"]
[null,"Results","From the table of survival probabilities, you can see that 88.63% survive more than 450 hours."]
["Nonpara Dist Analysis (Arbitrary)","Title","If you have uncensored or arbitrarily censored data and no distribution fits your data, the Nonparametric Distribution Analysis can be used to estimate cumulative failure probabilities, hazard rates and draw survival, cumulative failure and hazard plots."]
[null,"How to","• Choose ProcessMA > Reliability and Survival > Distribution Analysis (Arbitrary Censoring) > Nonparametric Distribution Analysis\n• In Start, select the column containing start times (Numeric, Use * to represent left-censored data) \n• In End, select the column containing end times (Numeric, Use * to represent right-censored data) \n• In Frequency, select the column containing frequency counts (Optional, Positive integer) \n• Under Estimate Tab, in Confidence Level, enter the desired confidence level (Numeric, >0 & <1)\n• Under Graph Tab, check Survival Plot, if you want to display survival plot\n• Under Graph Tab, check Cumulative Failure Plot, if you want to display cumulative failure plot\n• Under Graph Tab, check Show Confidence Interval, if you want to display confidence interval in the above plots \n• Click OK"]
[null,"Example","You work in a manufacturing plant making widgets and you want to find out the times at which widgets will fail. You have inspected the widgets at regular times (every 100 hours) to see how many have failed.\n• Open data worksheet by choosing ProcessMA > Tools > Data\n• Choose ProcessMA > Reliability and Survival > Distribution Analysis (Arbitrary Censoring) > Nonparametric Distribution Analysis\n• In Start, select CF - Start \n• In End, select CG - End \n• In Frequency, select CH - Frequency \n• Click OK"]
[null,"Results","From the Turnbull Estimates table, 13.58% of widgets are estimated to fail between 500 to 600 hours. From the survival probabilities, 94.3% of widgets are estimated to survive until 300 hours."]
["Accelerated Life Testing","Title","The Accelerated Life Testing is used to model failure times for products with high reliability."]
[null,"Details","The product is placed under high stress conditions, called accelerating variable, to accelerate the failure process. The failure times observed can then be used to estimate the failure times at normal conditions. Accelerated test can help to save time and money to study a product that will take a long time to reach failure at normal conditions. You can use ProcessMA Accelerated Life Testing to model uncensored/right censored data with one of the seven distributions (Weibull, Exponential, Normal, Lognormal, Logistic, Loglogistic, Smallest Extreme Value). In order to perform accelerated tests, you need to know the relationship between the accelerating variable and failure times. You can choose one of the following relationships:\n• Linear - no transformation, assumes change in failure time is proportional to accelerating variable \n• Arrhenius - commonly used to model failure as a result of a chemical reaction which depends on temperature \n• Inverse Temp - assumes failure time is inversely proportional to temperature (Kelvin) \n• Ln(Power) transformation - commonly used to model failure times of product under constant stress \n\nProcessMA uses maximum likelihood estimates to model parameters. "]
[null,"How to","• Choose ProcessMA > Reliability and Survival > Accelerated Life Testing \n• In Variable, select the column containing the data (Numeric) \n• In Frequency, select the column containing frequency counts (Optional, Positive integer) \n• In Assumed Distribution, choose the distribution to fit \n• In Accelerating Variable, select the column containing accelerating variable (Numeric) \n• In Relationship, choose a relationship for the accelerating variable\n• Under Censor Tab, in Censor, select the column containing censoring indicator (Optional, Exactly 2 distinct values - censored and uncensored) \n• Under Censor Tab, in Censor Value, choose the indicator you use to indicate censoring\n• Under Result Tab, in New Predictor Values, enter a new predictor value of the accelerating variable, usually the design value or normal running conditions (Optional, Numeric)\n• Under Result Tab, in Est. Percentiles for Percent, enter the percent values you want to calculate percentiles. Use this to calculate the time for x% of units to fail. (Optional, Numeric, >0 & <100, Separate multiple entries with commas)\n• Under Result Tab, in Est. Survival Prob for Times, enter the time value you want to calculate survival probabilities. Use this to calculate the probability that the product will survive past a specific period of time. (Optional, Numeric, >0, Separate multiple entries with commas)\n• Under Result Tab, in Confidence Level, enter the desired confidence level (Numeric, >0 & <1)\n• Under Graph Tab, check Relation Plot, if you want to display the relationship between the accelerating variable and failure time\n• Under Graph Tab, check Probability Plot (Individual), if you want to display a probability plot for each level of the accelerating variable based on individual fits\n• Under Graph Tab, check Probability Plot (Fitted), if you want to display a probability plot for each level of the accelerating variable based on the fitted model\n• Under Graph Tab, check Standardized Residuals, if you want to display a probability plot for standardized residuals\n• Under Graph Tab, check Cox-Snell Residuals, if you want to display a probability plot for Cox-Snell residuals\n• Under Graph Tab, check Show Confidence Interval, if you want to display confidence interval in the above plots \n• Click OK"]
[null,"Example","You work in a manufacturing plant making widgets and you want to find out the deterioration of widgets. You tested the widgets at higher temperatures to accelerate deterioration and collected their failure times. You want to extrapolate to 50 degree Celsius, which are temperatures the widgets normally operate at. It is known that the relationship between temperature and failure time follows the Arrhenius relationship.\n• Open data worksheet by choosing ProcessMA > Tools > Data\n• Choose ProcessMA > Reliability and Survival > Accelerated Life Testing \n• In Variable, select CI - Times \n• In Assumed Distribution, choose Weibull \n• In Accelerating Variable, select CJ - Temp \n• In Relationship, choose Arrhenius\n• Under Censor Tab, in Censor, select CK - Cen \n• Under Censor Tab, in Censor Value, choose C \n• Under Result Tab, in New Predictor Values, enter 50 \n• Under Graph Tab, check Probability Plot (Fitted)\n• Click OK"]
[null,"Results","From the table of percentiles, you can see that at 50 degrees Celsius, widgets will last 150966 hours at 50% percentile. \nNote: Y-axis of relation plot and X-axis of probablity plot is manually changed to log scale. "]
["Regression with Life Data","Title","The Regression with Life Data is used to assess whether predictors affect failure time and ultimately develop a model that can be used to predict failure time."]
[null,"Details","The model can include single factor, single covariate, interaction terms and nested terms. You can use ProcessMA Regression with Life Data to model uncensored/right censored data with one of the seven distributions (Weibull, Exponential, Normal, Lognormal, Logistic, Loglogistic, Smallest Extreme Value).\n\nProcessMA uses maximum likelihood estimates to model parameters."]
[null,"How to","• Choose ProcessMA > Reliability and Survival > Regression with Life Data \n• In Response, select the column containing the response data\n• In Term 1 to Term 10 , select the column containing data for the respective model terms and choose if the term is a covariate or a factor (Covariate: Numeric)\n• In Model, enter the terms to be included in the model. The Model can include factors, covariates, interactions and nested term. Multiple terms must be separated by commas. Use * to represent interactions and () to represent nesting. The model must be hierachical, if an interaction term is included, all lower order interactions and main terms must also be included.\n• In Assumed Distribution, choose the distribution to fit\n• In Censor, select the column containing censoring indicator (Optional, Exactly 2 distinct values - censored and uncensored) \n• In Censor Value, choose the indicator you use to indicate censoring\n• Check Standardized Residuals, if you want to display a probability plot for standardized residuals\n• Check Cox-Snell Residuals, if you want to display a probability plot for Cox-Snell residuals\n• Check Show Confidence Interval, if you want to display confidence interval in the above plots\n• In Confidence Level, enter the desired confidence level (Numeric, >0 & <1)\n• Click OK"]
[null,"Example","You work in a manufacturing plant making widgets and you want to find out the deterioration of widgets. You want to know if you can predict failure times for widgets based on the temperature and the chamber it operates in. It is known that the relationship between temperature and failure time follows the Arrhenius relationship. \n• Open data worksheet by choosing ProcessMA > Tools > Data\n• Choose ProcessMA > Reliability and Survival > Regression with Life Data \n• In Response, select CL - Times2 \n• In Term 1, select BN - Temp2 and choose Covariate\n• In Term 2, select BO - Chamber and choose Factor\n• In Model, enter Temp2, Chamber\n• In Assumed Distribution, choose Weibull \n• Under Censor Tab, in Censor, select CM - Cen2\n• Under Censor Tab, in Censor Value, choose C \n• Click OK"]
[null,"Results","From the regression table, you can obtain the coefficients for the regression model."]
["ProcessMA Interactive","Title","ProcessMA Interactive provides a realtime updated interface for ProcessMA tools"]
[null,"Details","When you create a new tool from ProcessMA interactive, a new pre-formatted worksheet will be created. As you enter data into designated columns, your analysis results will be computed and displayed dynamically. If charts are present, they will also dynamically plot and display the results. The following are the key features:\n\nAutomatic Re-calculation\nWith ProcessMA Interactive, analysis results are automatically re-calculated when you change your data and options without having to repeat the analysis process. \n\nDynamic Charts\nCharts are also dynamic. This feature is most useful for charts you need to update regularly such as the control charts. As you enter new data, the charts are dynamically re-plotted without the need to re-create them. \n\nCombining Related Tools in One\nRelated tools are now combined for easy access and to avoid duplication such as DOE (Design, Analyze & Factorial Plots), Power and Sample Size (All test types), etc "]
[null,"How to","Learning how to use ProcessMA Interactive is simple. Once you learn the know-how for one tool, the rest are similar. The following uses the Pareto Chart tool as an example to walkthrough the process.\n• Choose ProcessMA > Interactive\n• In Category, choose Graphs \n• In Tool, choose Pareto Chart \n• Check Load Example if you wish to populate worksheet with data for the example\n• Click OK\n\nA new pre-formatted spreadsheet will be created. Data must be entered in columns with the first row as the column label. Column labels can be changed as required Option fields are organized in rows with labels on the left and values on the right. As you enter data, the results are dynamically computed and displayed"]
[null,"How to","Data input limited to first 10,000 rows\nTo optimize speed, ProcessMA interactivity worksheets are limited to 10,000 rows of data input by default design. However, if you are familiar with User-Defined-Formula with array output, you can increase data input range to include the entire column. For example, to use the entire column for data input, you can change the UDF for Pareto Chart from \"=PMAPareto(K1:K10000,L1:L10000,I2)\" to \"=PMAPareto(K:K,L:L,I2)\". To change the UDF, first highlight the entire range of target cells, then press F2, then modify the UDF and finally press Ctrl-Shift-Enter. \n\nSpeed up data entry\nIf you are performing complex analytical tools like General Linear Model or Accelerated Life Testing for a large amount of data, the auto-recalculation may slow down your data entry process. Therefore, if you are entering a large amount of data for analysis, you can temporary switch Excel calculation option to Manual during data entry. When you have completed the data entry, switch Excel calculation option back to Automatic or press F9 to calculate the results. See the following instruction to change Excel Calculation Option to Manual \n\nPlotting more data points\nMost ProcessMA Interactive charts are set up by default to plot limited data points. If you need to plot more data points, you need to extend the respective formula array. To do so, go the first cell containing the formula array, select a large rows of cells, hit \"F2\" followed by \"CTRL+SHIFT+ENTER\". Note: Worksheets must be unprotected first \n\nSharing ProcessMA worksheets\nUsers need to have ProcessMA installed on their computers in order to update and use the Interactive worksheets and charts created by ProcessMA. You can share these worksheets with non ProcessMA user for viewing only, however, they should NOT update links when opening the workbooks. \n\nProtection\nWorksheets can be protected to prevent unintended changes. In a protected worksheet, only cells that require inputs will be accessible"]
[null,"Results","You collected data on time (in minutes) to resolve a customer enquiry in a call centre. You want to describe this set of data. You want to use ProcessMA Interactive tool because you intend to collect and add more data in the next few days.\n• Choose ProcessMA > Interactive\n• In Category, select Statistics\n• In Tool, select Descriptive Statistics\n• Enter data in Variables"]
["Tool Selector","Title","The tool selector can help you to select the appropriate tool in ProcessMA based on your objective and data type."]
[null,"Details","You can select the tool by Six Sigma DMAIC phases or by functional categories. "]
[null,"How to","• Choose ProcessMA > Tools > Tools Selector > By DMAIC or By Function \n• Click on the left-hand side buttons to select tools for that category.\n• Click on the flow diagram based on your objective and/or data type (current selection is highlighted in blue) \n• Click on the right-hand side buttons to launch the desired tool\n• The selected tool will be launch automatically. ProcessMA will return you to the Tool Selector again once you are done.\n• To close the Tool Selector, press ESC or Close the dialog box."]
["Worksheet Manager","Title","The Worksheet Manager is a tool to help you to organize and locate worksheets easily.\n"]
[null,"How to","To launch the worksheet manager, choose ProcessMA > Tools > Worksheet Manager. Read the following instructions to operate the tool: \n• Create New Folder: Select where you want the new folder to be located and click New Folder. Enter folder name in the inputbox and click OK. \n• Delete Folder: Select the folder you want to delete and click Delete Folder.\n• Rename Folder: Select the folder and then Rename Folder. Enter new folder name in the inputbox and click OK. \n• Move Down: Click to move worksheet or entire folder down. It can also be used to move the last worksheet in a folder out of it or move the a preceding worksheet into a folder. \n• Move Up: Click to move worksheet or entire folder up. It can also be used to move the first worksheet in a folder out of it or a subsequent worksheet into a folder.\n• Select Worksheet: Double-click on any worksheet name to select it."]
["End"]

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["#1#Title","10|4","To add a child node, enter text in the cell below the parent node"]
[null,null,"To delete a node, enter '#' in the cell below the node you wish to delete"]
[null,null,"To change a node, enter '\\' followed by the new text in the cell below the node you wish to change"]
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["Standard Height of Symbol",null,null,null,null,null,null,null,4]
["Standard Width of Symbol",null,null,null,null,null,null,null,6]

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[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Process Step / Input","Failure Mode","Effect of Failure","S","Potential Cause of failure","O","Current Detection Mechanism","D","RPN (S*O*D)","Preventive Actions","S","O","N","RPN (S*O*D)"]
[null,"Fishbone Diagram",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"BC2*BE2*BG2","v":0},null,null,null,null,{"$f":"BJ2*BK2*BL2","v":0}]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Process Step","Failure Mode","Potential Causes","Scoring",null,null,"Decision Tree Analysis",null,null,null,"Action Type","Actions or Rationale for Stopping","Outcome Measure","Person Responsible","Management Concurrence"]
[null,null,null,null,null,null,null,"Measurement",null,null,null,null,null,null,null,null,null,null,null,"Material",null,null,null,null,null,null,null,null,null,null,null,"Method",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Severity","Probability","Hazard Score","Single Point Weakness?","Existing Control Measure?","Detectable?","Proceed?"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"IF(OR(ISBLANK(BC6),ISBLANK(BD6)),\"\",LEFT(BC6,1)*LEFT(BD6,1))","v":""},null,null,null,{"$f":"IF(BE6>=8,IF(AND(BG6=\"N\",BH6=\"N\"),\"Y\",IF(AND(BG6<>\"\",BH6<>\"\",BE6<>\"\"),\"N\",\"\")),IF(AND(BF6=\"Y\",BG6=\"N\",BH6=\"N\"),\"Y\",IF(AND(BF6<>\"\",BG6<>\"\",BH6<>\"\",BE6<>\"\"),\"N\",\"\")))","v":""}]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Solution","Does it solve the problem?","Business Gains   \n(1-Low, 10 High)","Implementation  \n(1-Easy, 10-Difficult)","Priority"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"IF(AND(ISBLANK(BB9)=FALSE, ISBLANK(BC9)=FALSE),IF(BC9<=5,IF(BB9>=5,1,2),IF(BB9>=5,3,4)),\"\")","v":""}]
[]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Project Title"]
[]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"1. Background"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Problem"]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"2. As-Is State"]
[]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"3. Root Cause Analysis"]
[]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"4. To-Be State"]
[]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"5. Improvement Plan"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"What","Who","When","Status"]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Cost"]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"6. Monitoring"]
[null,null,null,null,null,null,null,"Environment",null,null,null,null,null,null,null,null,null,null,null,"Manpower",null,null,null,null,null,null,null,null,null,null,null,"Machine",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Plan",null,"Actual Results"]
[]
[]
[]
[]
[null,"Fishbone Diagram"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Process","Process Step/Activity","Input","Output","Specification Limits or Target Performance","Measurement Technique or Method of Evaluation","Sample Size","Sample Frequency","Person Responsible for Reporting","Action Plan","Remarks"]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,"Policy",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Procedure"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Activity","Description","Waste",null,null,null,null,null,null,"Description of waste"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Waiting","Transportation / Handling","Over processing","Useless Motion","Defective units","Excess Inventory","Overproduction"]
[]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Activity","Description","Does customer see value or be willing be pay for this activity?","Is this activity required if prior activities are done correctly or differently?","Does this activity physically change the product / service?","Is this activity dictated by policies and regulations?","VA / NVA / VE"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"IF(COUNTBLANK(BB47:BE47) =0,IF(ISERROR(MATCH(\"No\",BB47:BD47,0)),\"VA\",IF(ISERROR(MATCH(\"Yes\",BE47:BE47,0)),\"NVA\",\"VE\")),\"\")","v":""}]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"What to measure","Measurement Type","Operational Definition","Data Source","Collection Method","When","Measurement System","Display"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"What data do you need to answer the question? Stratification factors should be included.","Outcome or Variables, Continuous or Discrete","Precise description the value can be derived","Where is the data?  (E.g. Systems, case files)","Who and how will the data be collected?","Time span for historical data or at the point of activity?","How do you control measurement errors?","How will the data be displayed?"]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Problem"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Supplier","Input","Process",null,"Output","Customer"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Providers of resources","Resources required by process","Input specifications","High level description of activities","Deliverables of the process","Customer requirements on output","Stakeholders who receives the output"]
[]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Project Name"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Project Timeline","Start Date"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Completion Date"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Project Team","Leader"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Sponsor"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Members"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Coach"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Target Process"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Business Case"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Problem Statement"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Financial Savings"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Objective / Outcome","Metric (Ys)","Baseline","Goal"]
[null,null,null,null,null,null,null,null,null,null,null,null,"People",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Place"]
[]
[]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Project Scope","Start point"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"End point"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"In-scope"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Out-scope"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Milestones","Kickoff"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Define Complete"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Measure Complete"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Analyse Complete"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Improve Complete"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Control Complete"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Roles and Responsibilities","Name","Responsibilities"]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Resources Required"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Potential Barriers & Risks","Barriers and Risks","Strategies"]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Communication Plan","What to communicate","Who to communicate to","When to communicate"]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Area"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Date"]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"5S","Average Score"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Minimum",1,2,3,4]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Sort",null,{"$f":"IF(ISERROR(AVERAGE(BB132:BB135)),\"\",AVERAGE(BB132:BB135))","v":""},{"$f":"IF(ISERROR(AVERAGE(BC132:BC135)),\"\",AVERAGE(BC132:BC135))","v":""},{"$f":"IF(ISERROR(AVERAGE(BD132:BD135)),\"\",AVERAGE(BD132:BD135))","v":""},{"$f":"IF(ISERROR(AVERAGE(BE132:BE135)),\"\",AVERAGE(BE132:BE135))","v":""}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Set in order",null,{"$f":"IF(ISERROR(AVERAGE(BB136:BB139)),\"\",AVERAGE(BB136:BB139))","v":""},{"$f":"IF(ISERROR(AVERAGE(BC136:BC139)),\"\",AVERAGE(BC136:BC139))","v":""},{"$f":"IF(ISERROR(AVERAGE(BD136:BD139)),\"\",AVERAGE(BD136:BD139))","v":""},{"$f":"IF(ISERROR(AVERAGE(BE136:BE139)),\"\",AVERAGE(BE136:BE139))","v":""}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Shine",null,{"$f":"IF(ISERROR(AVERAGE(BB140:BB143)),\"\",AVERAGE(BB140:BB143))","v":""},{"$f":"IF(ISERROR(AVERAGE(BC140:BC143)),\"\",AVERAGE(BC140:BC143))","v":""},{"$f":"IF(ISERROR(AVERAGE(BD140:BD143)),\"\",AVERAGE(BD140:BD143))","v":""},{"$f":"IF(ISERROR(AVERAGE(BE140:BE143)),\"\",AVERAGE(BE140:BE143))","v":""}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Standardize",null,{"$f":"IF(ISERROR(AVERAGE(BB144:BB147)),\"\",AVERAGE(BB144:BB147))","v":""},{"$f":"IF(ISERROR(AVERAGE(BC144:BC147)),\"\",AVERAGE(BC144:BC147))","v":""},{"$f":"IF(ISERROR(AVERAGE(BD144:BD147)),\"\",AVERAGE(BD144:BD147))","v":""},{"$f":"IF(ISERROR(AVERAGE(BE144:BE147)),\"\",AVERAGE(BE144:BE147))","v":""}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Sustain",null,{"$f":"IF(ISERROR(AVERAGE(BB148:BB151)),\"\",AVERAGE(BB148:BB151))","v":""},{"$f":"IF(ISERROR(AVERAGE(BC148:BC151)),\"\",AVERAGE(BC148:BC151))","v":""},{"$f":"IF(ISERROR(AVERAGE(BD148:BD151)),\"\",AVERAGE(BD148:BD151))","v":""},{"$f":"IF(ISERROR(AVERAGE(BE148:BE151)),\"\",AVERAGE(BE148:BE151))","v":""}]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"5S","Descriptions","Score"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,1,2,3,4]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Sort","Only required documents are present (Documents not required have been stored)"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Only required office equipment are present (obsolete and unservicable equipment have been removed)"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Information on walls and bulletin boards are up-to-date and relevant"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Aisles and stairways are free of items"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Set in order","Storage locations (cabinets, drawers, etc) are clearly labelled and organised"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Items can be easily identified if misplaced or not returned to correct location"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Office equipment have a designated location and are easily accessible"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Emergency equipment (fire hoses, extinguishers, etc) are prominently displayed and easily accessible"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Shine","Office equipment are clean and in good working condition"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Cabinets, shelves and desks are tidy and clean"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Floors are clean and free of debris and boxes"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Garbage are collected and disposed properly"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Standardize","Office equipment are returned to the correct location immediately after use"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Office supplies (paper, toner, stationary) are adequate"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Office equipment maintenance records are visible where previous and next maintenance are scheduled"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"The previous 5S audit results are visible and recommendations have been actioned"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Sustain","All staff regularly conduct their own 'self-audit' so that deviations can be identified and actioned"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Manager visits the work area and pays attention to 5S results"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"5S documentation and instructions are up-to-date"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"5S audits are conducted regularly"]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Date","5S Audit Recommendation"]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Score","Description"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,0,"There is no 5S activity for this criteria"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,1,"5S effort is not organized and is likely the work of a few people"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,2,"Some 5S attempts but efforts are temporary and/or superficial"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,3,"All staff is improving 5S and previous improvements have become standard practices"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,3.5,"5S efforts are excellent although there are still some room for improvement"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,4,"Awarded after 3 consecutive scores of 3.5"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,4.5,"5S efforts are world-class and is fully institutionalized"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,5,"Awarded after 6 consecutive scores of 4.5"]
[]
[]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Takt Time Calculator"]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"No. of shift per day"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Available time per shift",null,"hours"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Downtime per shift",null,"hours"]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Customer demand per day",null,"unit"]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Takt Time",{"$f":"IF(BC191<>0,ROUND(((BC188-BC189)*BC187)*3600/BC191,2),\"\")","v":""},"seconds /  unit"]
[]
[]
[]
[]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Power and Sample Size Calculator"]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"1-Sample Z",null,null,"1 Proportion"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Standard Deviation",null,null,"Hypothesized p"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Alternate","Not equals",null,"Alternate","Not equals"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Significance Level",0.05,null,"Significance Level",0.05]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Sample Size",null,null,"Sample Size"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Difference",null,null,"Alternate Value of p"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Power Value",null,null,"Power Value"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Result",null,null,"Result"]
[]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"1-Sample t",null,null,"2 Proportions"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Standard Deviation",null,null,"Proportion 2"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Alternate","Not equals",null,"Alternate","Not equals"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Significance Level",0.05,null,"Significance Level",0.05]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Sample Size",null,null,"Sample Size"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Difference",null,null,"Proportion 1 Value"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Power Value",null,null,"Power Value"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Result",null,null,"Result"]
[]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"2-Sample t",null,null,"One-Way ANOVA"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Standard Deviation",null,null,"Standard Deviation"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Alternate","Not equals",null,"No. of Levels",2]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Significance Level",0.05,null,"Significance Level",0.05]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Sample Size",null,null,"Sample Size"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Difference",null,null,"Max Difference"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Power Value",null,null,"Power Value"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Result",null,null,"Result"]
[]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Continuous Data",null,null,"Discrete Data"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Standard Deviation",null,null,"Proportion"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Error/Difference",null,null,"Error/Difference"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Confidence Level",0.95,null,"Confidence Level",0.95]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Results",{"$f":"ABS(NORMSINV((1 - BC234) / 2))","v":1.9599639845400536},null,"Results",{"$f":"ABS(NORMSINV((1 - BF234) / 2))","v":1.9599639845400536}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Sample Size",{"$f":"IF(AND(ISBLANK(BC232)=FALSE,ISBLANK(BC233)=FALSE,ISBLANK(BC234)=FALSE),ROUND((BC235*BC232/BC233)^2,0),\"\")","v":""},null,"Sample Size",{"$f":"IF(AND(ISBLANK(BF232)=FALSE,ISBLANK(BF233)=FALSE,ISBLANK(BF234)=FALSE),ROUND((BF235/BF233)^2*BF232*(1-BF232),0),\"\")","v":""}]
[]
[]
[]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Sigma Calculator (Basic)"]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Data"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"No. of Opportunities"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"No. of Defects"]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Results"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"%Defects",{"$f":"IF(AND(ISBLANK(BC245)=FALSE,ISBLANK(BC244)=FALSE),BC245/BC244,\"\")","v":""}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"%Yield",{"$f":"IF(AND(ISBLANK(BC245)=FALSE,ISBLANK(BC244)=FALSE),1-BC245/BC244,\"\")","v":""}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"DPMO",{"$f":"IF(AND(ISBLANK(BC245)=FALSE,ISBLANK(BC244)=FALSE),BC245/BC244*1000000,\"\")","v":""}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Sigma",{"$f":"IF(AND(ISBLANK(BC245)=FALSE,ISBLANK(BC244)=FALSE),IF(BC245/BC244=0,\"+Infinity\",IF(BC245/BC244=1,\"-Infinity\",NORMSINV(1-BC245/BC244)+1.5)),\"\")","v":""}]
[]
[]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Sigma Calculator (Advanced)"]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Data"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"No. of Units"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"No. of Opportunities per Unit"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"No. of Defects"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Sigma Shift",1.5]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Results"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"%Defects",{"$f":"IF(AND(ISBLANK(BC258)=FALSE,ISBLANK(BC259)=FALSE,ISBLANK(BC260)=FALSE,ISBLANK(BC261)=FALSE),BC260/(BC259*BC258),\"\")","v":""}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"%Yield",{"$f":"IF(AND(ISBLANK(BC258)=FALSE,ISBLANK(BC259)=FALSE,ISBLANK(BC260)=FALSE,ISBLANK(BC261)=FALSE),1-BC260/(BC259*BC258),\"\")","v":""}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"DPU",{"$f":"IF(AND(ISBLANK(BC258)=FALSE,ISBLANK(BC259)=FALSE,ISBLANK(BC260)=FALSE,ISBLANK(BC261)=FALSE),BC260/BC258,\"\")","v":""}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"DPMO",{"$f":"IF(AND(ISBLANK(BC258)=FALSE,ISBLANK(BC259)=FALSE,ISBLANK(BC260)=FALSE,ISBLANK(BC261)=FALSE),BC260/BC258/BC259*1000000,\"\")","v":""}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Sigma",{"$f":"IF(AND(ISBLANK(BC258)=FALSE,ISBLANK(BC259)=FALSE,ISBLANK(BC260)=FALSE,ISBLANK(BC261)=FALSE),IF(BC260/(BC259*BC258)=0,\"+Infinity\",IF(BC260/(BC259*BC258)=1,\"-Infinity\",NORMSINV(1-BC260/(BC259*BC258))+BC261)),\"\")","v":""}]