Bayesian Modeling of Accelerated Life Tests with Random Effects

By
Avery J. Ashby
Ramón V. León
Jayanth Thyagarajan
Department of Statistics, The University of Tennessee, Knoxville. 37996-0532

Abstract
We show how to use Bayesian modeling to analyze data from an accelerated life test
where the test units come from different groups (such as batches) and the group effect is
random and significant. Our approach can handle multiple random effects and several
accelerating factors. However, we present our approach on the basis on an important
application concerning pressure vessels wrapped in Kevlar 49 fibers where the fibers of
each vessel comes from a single spool and the spool effect is random. We show how
Bayesian modeling using Markov chain Monte Carlo (MCMC) methods can be used to
easily answer questions of interest in accelerated life tests with random effects that are
not easily answered with more traditional 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
2 approach is implemented in the freely available WinBUGS software so that readers can
easily apply the method to their own data.

Keywords: Markov chain Monte Carlo (MCMC), WinBUGS, Credibility Interval,
Prediction Interval, Quantile.

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