Bayesian modeling of accelerated life tests with random effects

Abstract

We show how to use Bayesian methods to make inferences from an accelerated life test where the test units come from different groups (such as batches) and the group effect is random and significant both statistically and practically. Our approach can handle multiple random effects and several accelerating factors. We illustrate the method with an application concerning pressure vessels wrapped in Kevlar 49 fibers, where the fiber of each vessel comes from a single spool and the spool effect is random. We show how Bayesian analysis using Markov chain Monte Carlo (MCMC) methods is used to answer questions of interest in accelerated life tests with random effects that are not as easily answered with more traditional frequentist methods. For example, we can predict the lifetime of a pressure vessel wound with a Kevlar 49 fiber either from a spool used in the accelerated life test or from another random spool from the population of spools. We comment on the implications that this analysis has on the estimates of reliability (and safety) for the Space Shuttle, which has a system of 22 such pressure vessels. Our approach is implemented in the freely available WinBUGS software so that readers can apply the method to their own data.