Three questions related to JMP17's AIAG Gauge R&R Results optionI watched Hyde Miller-san's tutorial video for JMP17's MSA with my colleagues at JMP Japan office.
We have three questions about AIAG's Gauge R&R on JMP.
(1) On page.196 in AIAG(2010:4th ed.) Measurment System Analysis Reference Manual(4th ed.), it's said that "For analysis purposes, the negative variance component is set to zero". Does this sentece mean which of the followings?
- (a) You just set zero only for negative variance estimates, and calculate Gauge R&R indicies without changing positive variance estimates,...or...
- (b) You remove the components which has negative variance estimates, and refit the model.
(2)What kind of estimation method is used in JMP17's AIAG Gauge R&R Results on the EMP MSA platform?
Is the method REML/EMS *?
* If data is balanced and there is no negative variance, then EMS is used. Othewise, REML is used.
(3) I personally and intuitively think Bayesian analysis is generally better for MSA (because the sample size is not large in MSA study, and we can avoid negative estimates in Bayesian analysis). Is there a formal guideline or an academic refereed paper in which Bayesian analysis is recommended for MSA and/or Gauge R&R?
Re: Three questions related to JMP17's AIAG Gauge R&R Results optionThank you again, Michelson-san
I now understand the difference between the methods in AIAG MSA 4th ed. and JMP's ones. I will also check papers you had mentioned in the first reply and the JMP's course materials for understanding more.
Re: Three questions related to JMP17's AIAG Gauge R&R Results option1) When I worked for the semiconductor industry consortium, International SEMATECH, a team of statisticians from the international companies wrote a letter to AIAG, asking them to start a conversation with us about a more modern MSA guidelines book. This was during the time of the 3rd edition. They sent us back a rude letter and created the 4th edition without our input. This is from an organization who writes quality systems documents! Step 1 is always to find out what your customer wants! But they did not.
2) I also believe EMP uses REML only. You can use the Analysis Settings button in Variability to fit both Bayesian and REML models. Use JMP > Help > Sample Index > Measurement Systems > 3 Factors Crossed & Nested. The Bayesian and REML estimates are different. Then in EMP, the variance components match those found by REML in Variability. Even if you change your Variability preferences to use Bayesian, the EMP platform uses REML.
3) I entered the wrong link for the course materials. The correct link for internal use only is https://www.jmp.com/en_us/training/course-resources/measurement-system-analysis-course-resources.html.
Re: Three questions related to JMP17's AIAG Gauge R&R Results optionThank you very much for your reply, Michelson-san
(1) Some Japanese users just want to follow the guideline even if it's out of date. I personally think that (b)REML with positive constraints is better than (a), and Bayesian method is better than (b). But if they are not written in the guideline, it seems that some Japanese users don't want to use them. I hope that the next edition (5th ed) of AIAG MSA document become more modern. Anyway, thank you for information.
(2) My question is regard to "AIAG Gauge R&R Results" command of JMP17's EMP MSA. In JMP17's EMP MSA, we now have this command. I cannot find which estimation is used there. I wildly guess REML/EMS is used there, but I don't have confidence.
(3) Thank you again for information. I will check those papers refered by JMP's document, and I will ask to my manager and my collegues at JMP Japan how to get the JMP's course materials.
Re: Three questions related to JMP17's AIAG Gauge R&R Results optionI will try to partially answer.
1) The answer is a). Not a satisfying answer, because how can it be? What does it mean to get a negative variance? How can we just ignore that information and set it to zero? These are interesting and relevant questions, but I have not seen any papers discuss them. There are heavy theoretical statistical books (Hocking, Linear Models) that explain that variances are simply covariances, and by reparameterizing the model as a covariance model, the negatives make sense. But that doesn't help an engineer. In my experience (20 years in semiconductor, 10+ in JMP Education), negative variances happen with REML or EMS because the repeatability is small compared with variance from gauge study factors. You can check a box in Fit Model to restrict to non-negative variance components, but again, in my experience, with this method, you end up with zero variances and physically we know that variance is not zero.
2) AIAG Gauge R&R Analysis allows you to specify the method on the launch dialog, same as Variability. Use the Analysis Settings button to specify.
3) I agree. The negative variance components using REML or EMS come out to be small using the Bayesian method. There are two references in the JMP documentation that sound like they are relevant. (My JSTOR doesn't work right so I can't look them up right now)
Portnoy, S. (1971). “Formal Bayes Estimation with Application to a Random Effects Model.” The Annals of Mathematical Statistics 42:1379–1402.
Sahai, H. (1974). “Some Formal Bayes Estimators of Variance Components in the Balanced Three-Stage Nested Random Effects Model.” Communication in Statistics – Simulation and Computation 3:233–242.
Internal JMP employees can access our MSA course materials that might have more detail at
https://www.jmp.com/en_us/training/courses/jmp-measurement-system-analysis.html
