Gabriel Murray writes:

I saw this post and response from about 5 years ago, regarding a fellow analyzing levels of white blood cells.

He was asking about Bayesian approaches to quality control and couldn’t find a canonical resource on that topic. Five years on and I similarly don’t see many good resources on the topic, though it seems like a useful application of Bayesian analysis. Just wondering if you have any further thoughts on the matter now after a few years.

In my searching, I did find this interesting book on Bayesian Reliability. It’s not quality control, of course, but it does seem that failure prediction and risk analysis have some bearing on quality control and process control. And the cited reviews are very positive. It was written by some researchers at Los Alamos.

Also an edited book on process control: I saw that Bill Bolstad gives it a positive review in one of the journals. And a book on Bayesian risk analysis.

The comment from the original post about using a continuous measure rather than a binary measure is important for understanding the issue raised. The minimum sample size requirements for control charts that measure “non-conformities” (errors) are based on the average non-conformity rate in the process being measured. Lower error rates require larger sample sizes to make valid inferences because of the properties of the binomial distribution. I’m not sure how Bayesian methods can address this original sample size issue raised, but would love to hear!

I studied statistics whilst working as an engineer involved in quality assurance (including applying standard SQC measures), and when originally learning about Bayesian statistics I thought there was an obvious advantage in terms of using informative priors from relative ‘fast’ processes to speed convergence of relatively ‘slow’ processes. In my own case, I was working with extrusions with very thick walls where non-conformities came approximately once or twice a month, but at the same linear rate as a thinner wall process on the same site producing non-conformities at once or twice a week. Then at least the control lines could be set much more quickly, giving you a chance of evaluating improvement measures faster than after a couple of years.

Thanks for posting this, Andrew. As a follow-up, I can report that “Bayesian Reliability” by Hamada et al. is really excellent. And the first few chapters that give a general introduction to Bayesian stats and MCMC are amongst the best intros I have seen. The Kelly & Smith book, in contrast, gives some nice examples and sample code but is very light on theory.