Hi Simone
Thanks for sharing the Minitab results.
JMP has two places where you can perform process capability. The Distribution platform and the Process Capability platform (under Analyze>Quality and Process).
You've used the distribution platform, which is the platform that I prefer to use. However, the Process Capability platform provides additional options for computing capability indices for non-normal distributions (note to self: this seems to be true also for v15 of JMP which has had process capability overhauled in the distribution platform.
The key point is this. In the Process Capability platform you can two different types of calculation:
Switching to Z-score gives the same result as Minitab.
This hopefully explains the difference - although begs the bigger question of which method to use (coincidentally I am currently investigating this same question but as of yet I'm not in a position to express an opinion - having said that, if you transform the data the result for this data is comparable to the Z-score result).
-Dave