A semiparametric Bayesian generalized linear mixed model for the reliability of Kevlar fibres
Wednesday 30th March 2011
Argiento, R.; Guglielmi, A.; Soriano J.
We analyze the reliability of NASA composite pressure vessels using a new Bayesian semiparametric model. The dataset consists of lifetimes of pressure vessels, wrapped with a Kevlar ﬁber, grouped by spool, subject to different stress levels; 10% of data are right censored. The model we consider is a regression on the log-scale for the lifetimes, with ﬁxed (stress) and random (spool) eﬀects. The prior of the spool parameters is nonparametric, namely they are a sample from a normalized generalized gamma process, which encompasses the well-known Dirichlet process. The nonparametric prior is assumed to robustify inferences to mispeciﬁcation of the parametric prior. Here, this choice of likelihood and prior yields a new Bayesian model in reliability analysis. Via a Bayesian hierarchical approach, it is easy to analyze the reliability of the Kevlar ﬁber by predicting quantiles of the failure time when a new spool is selected at random from the population of spools. Moreover, for comparative purposes we review the most interesting frequentist and Bayesian models analyzing this dataset. Our credibility intervals of the quantiles of interest for a new random spool are narrower than those derived by previous Bayesian parametric literature. Additionally, the discreteness of the random-eﬀects distribution induces a natural clustering of the spools into three diﬀerent groups, which is in accordance with the frequentist spool rankings.