Hi @s_ard ,
A quick Google search brought me to this JMP community article here and this JMP Blog, here, describing how to account for nonnormal distributions in the process capability platform using JMP 13 and higher. According to the blog, you can either specify the distribution based on your best fit results, or use the nonparametric method, which assumes no known distribution.
That being said, I think you should follow some of the suggestions from @cwillden in the community article about doing some background due diligence and additional investigation into the root cause of your normal 2 mixture distribution. For example, looking at a control chart, as he points out (as a side note, looking at the MDMVCC platform can be very useful in finding some outlier processes that might be causing nonnormal behavior.
As a descriptive example, you might have process that after running for months underwent some kind shift in the mean, let's say from 20 to 25, unknown to you (and all the material was still in spec). If you look the control chart, you might be able to determine when this shift took place, go back to production and see what changed. Let's say production found out they had a faulty flow meter and after swapping it out, they were getting the correct throughput, which resulted in the shift in mean. This might show up as a nonnormal distribution, but it can be explained by the two phases, and when addressed accordingly in the control chart will calculate the statistics for each phase. This would account for the change and give you the correct values for each phase.
If your process is such that it truly has a nonnormal distribution and must be accounted for in the process capability platform, there you would use your best fit distribution function and tell JMP directly what the distribution should be. JMP will then correctly calculate the relevant statistics.
But, as mentioned in the community article, stability is critical in using these indices correctly. If it's truly not stable and more due diligence is required, do that before trying to report a cpk value. If it is stable and this is really the distribution, then you need to tell JMP explicitly to use an alternative distribution. It's my understanding that the calculations are the same comparing the mean and standard deviations to the spec limits, but the different distributions will change the definition of what the mean is and what the standard deviations are that will be used to calculate cpk.
Hope this helps,
DS
