Colin Lewis-Beck | Searcharxiv

arXiv2022

Specifying Prior Distributions in Reliability Applications

Especially when facing reliability data with limited information (e.g., a small number of failures), there are strong motivations for using Bayesian inference methods. These include the option to use information from physics-of-failure or previous experience with a failure mode in a particular material to specify an informative prior distribution. Another advantage is the ability to make statistical inferences without having to rely on specious (when the number of failures is small) asymptotic theory needed to justify non-Bayesian methods. Users of non-Bayesian methods are faced with multiple methods of constructing uncertainty intervals (Wald, likelihood, and various bootstrap methods) that can give substantially different answers when there is little information in the data. For Bayesian inference, there is only one method of constructing equal-tail credible intervals-but it is necessary to provide a prior distribution to fully specify the model. Much work has been done to find default prior distributions that will provide inference methods with good (and in some cases exact) frequentist coverage properties. This paper reviews some of this work and provides, evaluates, and illustrates principled extensions and adaptations of these methods to the practical realities of reliability data (e.g., non-trivial censoring).

stat.ME↗

arXiv2020

Prediction of Future Failures for Heterogeneous Reliability Field Data

This article introduces methods for constructing prediction bounds or intervals for the number of future failures from heterogeneous reliability field data. We focus on within-sample prediction where early data from a failure-time process is used to predict future failures from the same process. Early data from high-reliability products, however, often have limited information due to some combination of small sample sizes, censoring, and truncation. In such cases, we use a Bayesian hierarchical model to model jointly multiple lifetime distributions arising from different subpopulations of similar products. By borrowing information across subpopulations, our method enables stable estimation and the computation of corresponding prediction intervals, even in cases where there are few observed failures. Three applications are provided to illustrate this methodology, and a simulation study is used to validate the coverage performance of the prediction intervals.

stat.ME↗