topic Re: Minitab and JMP: different results for CPK in Lognormal data in Discussions

Minitab and JMP: different results for CPK in Lognormal data

Simone1 — Fri, 09 Jun 2023 00:17:10 GMT

Dears,

in this moment I'm evaluating a set of data.

This data are lognormal distributed.

I perform the CPK analysis wiht JMP and with Minitab: the capability resutl is different.

Some one of you, knonw the reason?

I think it could be linked to the type of formula usage for capability calculation... but I'm not sure.

Thanks in advance for the feedback.

Best regards,

Simone

Re: Minitab and JMP: different results for CPK in Lognormal data

txnelson — Fri, 12 Jun 2020 09:57:46 GMT

Have you verified in the JMP and Minitab documentation, that the formula used for the calculation is supposed to be the same? Or do they have different ideas on what the calculation should be?

Re: Minitab and JMP: different results for CPK in Lognormal data

David_Burnham — Fri, 12 Jun 2020 13:20:42 GMT

What spec values are you using? What are the values of the capability indices reported by Minitab?

Re: Minitab and JMP: different results for CPK in Lognormal data

Simone1 — Sat, 13 Jun 2020 20:33:48 GMT

Hello Nelson,

I'm trying to do this.

To be honest I was not able to find the formua used in JMP.

Do you have some suggestion about where I can found it?

Thansk in advance.

Best Regards,

Simone

Re: Minitab and JMP: different results for CPK in Lognormal data

Simone1 — Sat, 13 Jun 2020 20:44:49 GMT

Dear David,

in attachment you can find the data used for this analysis.

You can also see the comparisono between Minitab and JMP on the same data set.

Thanks in advance for your feedback.

Best Regards,

Simone

Re: Minitab and JMP: different results for CPK in Lognormal data

David_Burnham — Sun, 14 Jun 2020 09:39:29 GMT

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).

Re: Minitab and JMP: different results for CPK in Lognormal data

Simone1 — Mon, 15 Jun 2020 13:42:05 GMT

Dear David,

Thanks for the GOOD Explanation!

I followed your suggestion also for other type of distribution (like Weibull).

There is a difference if I use Percentiles or Z-score (and with Z-score the results matchs with Minitab).

This is good... for the understanding: step 1.

Now coud be usefull to understand the differences of CPK resutls... according the difference in the "Capability Index Method": as you can image... in front of a discussion (with a customer or supplier)... this can create long long additional discussions.

Thanks.

Best Regards,

Simone

Re: Minitab and JMP: different results for CPK in Lognormal data

Laura_Lancaster — Mon, 15 Jun 2020 15:21:07 GMT

Hi Simone,

You can find the documentation about the two different methods for calculating nonnormal capability indices here. I hope that helps some. Also, starting with JMP 15, both of these methods for calculating nonnormal capability are available in the distribution platform as well for nonnormal distribution fits.

Laura

Re: Minitab and JMP: different results for CPK in Lognormal data

Simone1 — Tue, 16 Jun 2020 06:59:51 GMT

Dear Laura,

thanks for the details and feedback.

All is clear.

Have you a good day.

Best Regards,

Simone

Re: Minitab and JMP: different results for CPK in Lognormal data

David_Burnham — Tue, 16 Jun 2020 18:23:30 GMT

I also have a strong interest in understanding the differences. I'm currently doing some investigations into this area - I'll let you know when I've written them up.

Re: Minitab and JMP: different results for CPK in Lognormal data

Simone1 — Wed, 17 Jun 2020 07:03:25 GMT

Thanks for the feedback Dave.

Best Regards,

Simone

Re: Minitab and JMP: different results for CPK in Lognormal data

Mark_Bailey — Wed, 24 Jun 2020 11:23:02 GMT

I think that the key to understanding these methods and their differences is this statement from the cited JMP documentation: "However, unless you have a very large amount of data, a nonparametric fit might not accurately reflect behavior in the tails of the distribution."

So this situation is similar to reliability analysis. Most of the time in an analysis, the model is used for interpolation, but in reliability and capability, the emphasis is on extrapolation into the tails. The tails of the distribution are where the desired information resides. The parametric fit is more efficient (more information from less data). It is possible (i.e., sometimes) to fit a good parametric model (good estimates of the parameters) with only a handful of observations. This approach emphasizes the importance of your choice for the model and your belief in it.

For example, I fit several distribution models to the weight data in Big Class using the Life Distribution platform for illustration.

I chose the Normal scale to linearize the CDF in this case. The models are very similar over the range of probability from 0.3 to 0.9. They are practically indistinguishable in this range and all of them provide similar estimates by interpolation. What about the tails, though? Calculating the capability requires estimating the weight range of ±3σ, which on the normal scale corresponds to probabilities (1.0 - 0.9973) / 2 = 0.00135 and 1 - 0.00135 = 0.99865. These different models will give very different extrapolations of weight at those probabilities.

The symmetric normal distribution equates the mean and the median. Only the median is guaranteed to represent the center in a non-normal distribution. So the Percentile method is a direct translation of the capability indices.

The Z Score method instead translates the specifications to quantiles but this transformation will still depend on the choice of the model and extrapolation. The specification is first converted to a probability with the fitted distribution model. Then the probability is converted to a quantile from the standard normal distribution, so it can be compared to ±3.

Re: Minitab and JMP: different results for CPK in Lognormal data

Simone1 — Mon, 29 Jun 2020 21:13:45 GMT

Thanks Mark clear explanation.

As you can image, when we speak with some organizations/customer... the question is very "practical question": you have lognormal distribution... which is the Cpk value? And... it is not so easy to pass the message that you can have different Cpk according the methodology you use for the calculation.

Best Regards,

Simone

Re: Minitab and JMP: different results for CPK in Lognormal data

Mark_Bailey — Tue, 30 Jun 2020 12:00:04 GMT

Yes, I can appreciate the confusion as a JMP instructor!

That is why it is important for the customer to understand first what capability and performance indices are and second that there is more than one way to estimate them. If they ask for such indices, then they should have an idea about which way is best for them. Some industries have standards. Other industries and companies choose their own way. If the indices are to be used as important management data, then it is important for management to decide. They learn to understand and use complex financial data, indices, and calculations. Process information is no different.

Re: Minitab and JMP: different results for CPK in Lognormal data

statman — Tue, 30 Jun 2020 14:17:41 GMT

Mark is completely correct. There are a lot of papers on the subject.

Fred Spiring, Bartholomew Leung, Smiley Cheng and Anthony Yeung, Bibliography of Process Capability Papers,QUALITY AND RELIABILITY ENGINEERING INTERNATIONAL Qual. Reliab. Engng. Int. 2003; 19:445–460 (DOI: 10.1002/qre.538)

lists many of the papers on the subject.

Here is another with a good summary of issues:

http://www.stats.uwaterloo.ca/~shsteine/papers/cap.pdf

Re: Minitab and JMP: different results for CPK in Lognormal data

Simone1 — Tue, 30 Jun 2020 16:28:24 GMT

Thanks!

Best Regards,

Simone

Re: Minitab and JMP: different results for CPK in Lognormal data

David_Burnham — Tue, 30 Jun 2020 19:14:05 GMT

Simone is raising a very legitimate point. If for example, I look at the link provided by @statman then it states the common requirement of Ppk > 1.33, but then goes on to say that "process capability indices calculated from non-normal processes are not comparable with those from normal processes".

I've always tended to favour the ISO/Percentile method for generalising capability indices for non-normal distributions. The reason being, for me the mathematics is a logical extension of the original intent for the indices.

But as I work more with vendors within supply chains I see that the capability indices tend to be used as generic performance indicators, and often combined to form a decision matrix to prioritise engineering actions. Ppk (or Cpk, take your pick - that's a separate discussion!) are used as a proxy measure of non-conformance. On this basis it is better to generalise the capability index such that it can be interpreted reasonably independent of the underlying distribution type. I believe that is the underlying basis of the Z-score method; therefore I'm tending to think now that this is the preferable method of calculation.

There is a 3rd approach used by some quality practitioners, which is to transform the data e.g. box-cox transformation; I believe it is the case (I still need to double-check this) that if you transform the data (and specs) and perform process capability then you will get the same outcome as if you used the Z-score method of calculation; which is another argument in its favour.

ps: the original title of the post was a query of Minitab versus JMP. Both systems support both the ISO/Percentile method and the Z-score method. But whereas Minitab defaults to the Z-score method, JMP defaults to the ISO/Percentile method. In JMP, you can change the default behaviour by selecting File>Preferences>Platforms.