I am writing to inquire about calculating process capability indices for nonparametic methods
Within JMP's Process Capability Analysis platform, you can use the "Select Distribution" option to fit a specific distribution (e.g., Weibull, Lognormal) and then compute the process capability indices. Alternatively, you can select "Nonparametric" to compute the process capability indices without fitting a specific distribution.
I'm curious about how the process capability indices are calculated, especially when "Nonparametric" is selected in "Distribution Selection", because the results from JMP are different from the results I calculated myself.
My customer mentioned that it is difficult to understand how this result was obtained.
JMP describes two ways to compute capability indices without assuming a normal distribution (see link: https://www.jmp.com/support/help/en/18.0/index.shtml#page/jmp/statistical-details-for-capability-indices-for-nonnormal-distributions.shtml 
(1) the percentile method and (2) the Z-score method.
(1) Percentile method
The percentile method calculates the process capability index using the USL, LSL, 99.865, 50, and 0.135 percentiles as follows.
I am curious how JMP calculates these percentiles. To illustrate my question, I have attached a file where I calculated the 99.865th, 50th, and 0.135th percentiles for variable Y, which are 8.6, 8.3, and 8.1, respectively.
If USL = 9.9 and LSL = 6.9, we would expect Pp to be calculated as (USL - LSL) / (99.865th percentile - 0.135th percentile) = (9.9 - 6.9) / (8.6 - 8.1) = 3 / 0.5 = 6. However, the actual JMP output shows that Pp is 2.451.
When I select "Nonparametric", it seems like JMP uses a different method to calculate percentiles, resulting in different Pp values. Can you explain how these percentiles are calculated?
(2) Z-Score Method
In the description of the Z-Score method, it says that F is a suitable distribution, but I would like to know which distribution is suitable when “Nonparametric” is selected in “Distribution Selection”.
Thank you in advance for your help. I look forward to your reply.
thank you,
Hi @HyeWonJung ,
If you want to calculate Pp, you can do this as follows.
- Select Continuous Fit > Smooth Curve from the red triangle.
- From the red triangle next to "Nonparametric Density", select Quantile Profiler.
- Enter 0.00135 in the Probability Number edit box and you will get the quantile that JMP uses.
Regarding the z-score method, I think JMP always uses the F distribution when using z-score method.
I hope it helps.
Yuichi
Thank you.I can give the appropriate approach based on your answer!><
