On selection of optimal stochastic model for accelerated life testing

•Statistical survival and reliability analysis and Bayes approach.•Bayes semi-parametric regression modeling in Cox׳s and AFT models.•Bayes version of martingale residuals and goodness-of-fit test.

This paper deals with the problem of proper lifetime model selection in the context of statistical reliability analysis. Namely, we consider regression models describing the dependence of failure intensities on a covariate, for instance, a stressor. Testing the model fit is standardly based on the so-called martingale residuals. Their analysis has already been studied by many authors. Nevertheless, the Bayes approach to the problem, in spite of its advantages, is just developing. We shall present the Bayes procedure of estimation in several semi-parametric regression models of failure intensity. Then, our main concern is the Bayes construction of residual processes and goodness-of-fit tests based on them. The method is illustrated with both artificial and real-data examples.