A Bayes Analysis and Comparison of Arrhenius Weibull and Arrhenius Lognormal Models under Competing Risk

Abstract

Abstract The paper considers constant stress accelerated life test situations under a competing risk scenario. The different groups of experimental units are operated at different accelerated levels of stress and, at each level, the units are exposed to fail from two competing causes of failures. For modeling the failure times resulting from such a test, the paper considers two competing risk models. The first model is based on the minimum of two Weibull failure times whereas the second one is based on the minimum of two lognormal failure times. In order to study the effect of covariates on failure times, the scale parameter of component models in each modeling framework has been regressed using the Arrhenius relationship. The paper performs a complete Bayes analysis of both the considered models for a real dataset arising from a temperature accelerated life test experiment and compares the two models using a few standard Bayesian tools. Bayes analysis is done using vague but proper priors for the parameters. Moreover, the considered models result in to intractable posterior distributions and, therefore, the paper uses the Metropolis algorithm to draw the desired posterior based inferences. For censored data situations, however, the intermediate Gibbs steps are used as updating mechanism by defining full conditionals corresponding to unknown censored data. The plausibility of both the models for entertained dataset has also been checked before performing their comparison. A numerical example based on a real dataset is provided for illustration.