A semiparametric Bayesian generalized linear mixed model for the reliability of Kevlar fibers

Abstract

We analyze the reliability of NASA composite pressure vessels by using a new Bayesian semiparametric model. The data set consists of lifetimes of pressure vessels, wrapped with a Kevlar fiber, grouped by spool, subject to different stress levels; 10% of the data are right censored. The model that 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 misspecification 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 data set. Our credibility intervals of the quantiles of interest for a new random spool are narrower than those derived by previous Bayesian parametric literature, although the predictive goodnessof-fit performances are similar. Finally, as an original feature of our model, by means of the discreteness of the random-effects distribution, we are able to cluster the spools into three different groups.Appl. Stochastic Models Bus. Ind. 2013, 29 410-423 R. ARGIENTO, A. GUGLIELMI AND J. SORIANO and Kunz [2] fitted six separated (frequentist) regression models by using data from six spools only. Glaser [3] and Crowder et al. [4] fitted AFT models for the failure times by using Weibull distributions with both stress and spool as fixed effects. Feiveson and Kulkarni [5] were the first to emphasize the need of assuming the spool effect as random and provided a frequentist estimate of the parameters of the Weibull distribution for each stress level. Recently, Bayesian approaches were proposed to analyze the data set: Leon et al.[6] consider a Bayesian Weibull regression model with the spool random effect, whereas Argiento et al. [7] propose a semiparametric Bayesian Weibull regression model, where the random effect is not induced by the spool classification but is inferred via a discrete nonparametric component. In contrast, our semiparametric model provides new statistical findings, the most relevant being the clustering of the spools into three groups, as heuristically suggested by Crowder et al. [4], but here derived as an inferential result. Indeed, clusterization of the spools into a random partition is intrinsic to our model, thanks to the discreteness of the trajectories of the nonparametric component.As far as the statistical inference of this data set is concerned, the aim of this paper is twofold. On the one hand, we want to predict the reliability of the Kevlar yarn by using a Bayesian hierarchical approach to the problem. Und...

A “Density-Based” Algorithm for Cluster Analysis Using Species Sampling Gaussian Mixture Models

“…In this case, a deeper analysis on the prior elicitation could be accomplished. See for instance Argiento et al (2012) and Griffin (2010).…”