A Comparison of Two Modelling Approaches to Reliability Data

We consider two models for the failure time of Kevlar wrapped pressure vessels. A Bayesian approach is undertaken using Monte Carlo Markov Chains (MCMC) to find estimates for the model parameters using the Birnbaum-Saunders distribution. Credible intervals are also supplied as part of the study. In addition, various priors are used in the analysis for the purposes of comparison, and convergence diagnostics are studied. Inference on the various model parameters is also provided. This analysis is repeated using the lognormal distribution. Furthermore, an ordering of spools by strength is provided, and the deviance information criteria (DIC) is given as a way to compare the analysis under both distributions. We study the 0.01, 0.10, and 0.50 quantiles at various stress levels. The median failure times are given for the various spools along with upper and lower credible limits. This quantile analysis is also performed using both distributions, as is an examination of the survival probabilities at 10000 hours. This study is completed using an MCMC approach. A final analysis is conducted where a simulation is carried out with a focus on regression parameters. The simulation is performed using the MCMC procedure.