Bayesian Methods for Reliability Data

[NathanielF]

Notebook proposal

Bayesian Methods fo reliability Data

This topic crops up in engineering quite a bit and generally involves a spin on survival analysis (time to failure) type models, but it's also tightly linked with the notion of cost-benefit, since there is a tolerable degree of failure. I was thinking about riffing on a discussion about prediction intervals for failure analysis in:

https://www.wiley.com/en-us/Statistical+Methods+for+Reliability+Data,+2nd+Edition-p-9781118115459

and contrast the frequentist and Bayesian approach to calibrated prediction. It might be interesting to contrast conformal prediction methods too, since it is a frequentist approach to uncertainty quantification which is getting quite a bit of coverage lately.

Suggested categories:

• Level: Intermediate
• Diataxis type: explanation

Related notebooks

It might have cross over in themes with: #407
and some of the techniques for modelling the failure predictions draw on survival analysis models.

[OriolAbril]

I think it would be a great addition, and it is a great fit for an explanation type notebook (that can/could complement other how-to notebooks on generating predictions for different kind of models for example).

[NathanielF]

Did a little work on this over the Christmas holidays. Written up a brief discussion of nonparametric and parametric estimation of reliability distributions and their CDFs. I'm following an example in the book cited above which moves through the frequentist MLE style estimation to a data set with very few failures... it argues for the importance of Bayesian modelling in this case especially.... so I think it's a good example for here.

However, I'm stuck a bit on trying to replicate the model fits achieved in the book or bring them anywhere close to the MLE fits. I'm using a Weibull survival model and I've tried (a) to replicate the stan model they use in the book (b) just use a base pymc weibull fit adding a potential for lcdf portion of the log likelihood and (c) use the censored model transformation as discussed in one of the survival analysis notebooks by @drbenvincent . I've use both period form and item-period data sets as described in the notebook, but none seem to recover good model fits with the pymc implementation...

I reckon I must be doing something silly so would appreciate any pointers you might have.