Parametric Distribution Analysis (Arbitrary Censoring)

Overview | How to | Example

 

 

Overview

This tool performs Parametric Distribution Analysis for uncensored and arbitrarily censored data. 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.

 

 

How to

At the Excel Menu (For Excel 2007, go to Add-ins first)

  1. Choose ProcessMA > Reliability and Survival > Distribution Analysis (Arbitrary Censoring) > Parametric Distribution Analysis

  2. In Start, select the column containing start times (Numeric, Use * to represent left-censored data)

  3. In End, select the column containing end times (Numeric, Use * to represent right-censored data)

  4. In Frequency, select the column containing frequency counts (Optional, Positive integer)

  5. In Assumed Distribution, choose the distribution to fit

  6. Under Estimate Tab, in Estimation Method, choose the method used to estimate distribution parameters

  7. Under Estimate Tab, in Set Shape/Scale At, enter a known shape and scale parameter for the variable (Optional, Numeric)

  8. Under Result Tab, check Show Parameter Estimates, if you want to estimate distribution parameters

  9. Under Result Tab, check Show Characteristics, if you want to calculate distribution characteristics

  10. Under Result Tab, check Estimate Percentiles, if you want to calculate percentile values for specific percent

  11. Under Result Tab, in Percent, enter the percent values you want to calculate percentiles (Optional, Numeric, >0 & <100, Separate multiple entries with commas)

  12. Under Result Tab, check Estimate Survival Probabilities, if you want to calculate survival probabilities for values for specific times

  13. Under Result Tab, in Times, enter the time value you want to calculate survival probabilities (Optional, Numeric, >0, Separate multiple entries with commas)

  14. Under Result Tab, in Confidence Level, enter the desired confidence level (Numeric, >0 & <1)

  15. Under Graph Tab, check Probability Plot, if you want to display probability plot

  16. Under Graph Tab, check Probability Density Plot, if you want to display probability density plot

  17. Under Graph Tab, check Survival Plot, if you want to display survival plot

  18. Under Graph Tab, check Cumulative Failure Plot, if you want to display cumulative failure plot

  19. Under Graph Tab, check Hazard Plot, if you want to display hazard plot

  20. Under Graph Tab, check Show Confidence Interval, if you want to display confidence interval in the above plots

  21. Click OK

 

 

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.

  1. Open data worksheet by choosing ProcessMA > Tools > Data

  2. Choose ProcessMA > Reliability and Survival > Distribution Analysis (Arbitrary Censoring) > Parametric Distribution Analysis

  3. In Start, select CF - Start

  4. In End, select CG - End

  5. In Frequency, select CH - Frequency

  6. In Assumed Distribution, choose Smallest Extreme Value

  7. Under Result Tab, check Show Parameter Estimates

  8. Under Result Tab, check Show Characteristics

  9. Under Result Tab, check Estimate Percentiles

  10. Under Result Tab, check Estimate Survival Probabilities

  11. Under Result Tab, in Times, enter 450

  12. Click OK

 

Results & Interpretation

From the table of survival probabilities, you can see that 88.63% survive more than 450 hours.

 

 

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