The Capability Analysis (Between/Within) generates a process capability report containing various capability indices using both between-subgroup and within-subgroup variation. 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.
This 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.
Interpret Capability Indices
Cp |
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. |
Cpk |
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. |
Pp |
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. |
Ppk |
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. |
Z |
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. |
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. |
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. |
At the Excel Menu (For Excel 2007, go to Add-ins first)
Choose ProcessMA > Quality Tools > Capability Analysis > Capability Analysis (Between/Within)
In Variable, select the column containing the data (Numeric)
In Subgroup, select the column containing subgroup indicators (Optional, >=2 distinct values)
In Constant Subgroup Size, enter the subgroup size if it is constant (Optional, Integer, >=2)
In Lower Specification Limit, enter the lower specification limit (At least one limit is required, Numeric)
In Upper Specification Limit, enter the lower specification limit (At least one limit is required, Numeric)
In Historical Mean, enter the population proportion, otherwise it will be estimated from the sample (Optional, Numeric)
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)
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)
In Target, enter the target value. It is used to calculate Cpm (Optional, Numeric)
In Sigma Tolerance, enter the interval (number of standard deviations) to calculate the capability statistics, otherwise 6 standard deviations will be used (Numeric, >0)
In Method (Subgroup>1), choose the method of estimating sigma when subgroup size is greater than 1
In Method (Subgroup=1), choose the method of estimating sigma when subgroup size is equals to 1
In Moving Range Length, enter the number of observations used to calculate the moving range (Integer, >=2)
In Display Capabilities in, choose the method to display capability indices
In Display Performance in, choose the method to display performance indices
Click OK
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.
Open data worksheet by choosing ProcessMA > Tools > Data
Choose ProcessMA > Quality Tools > Capability Analysis > Capability Analysis (Between/Within)
In Variable, select D - Diameter
In Constant Subgroup Size, enter 10
In Lower Specification Limit, enter 298
In Upper Specification Limit, enter 302
In Target, enter 300
Click OK
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.
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