This paper looks into the Bayesian approach for analyzing and selecting the bestPoisson process model for grouped failure data from a repairable system with covariate. Theextended powerlaw model with a recurrence rate that incorporates both time and covariateeffect is compared to the powerlaw, log-linear and HPP models. We propose the use ofboth informative and noninformative priors depending on the nature of the parameter. TheMCMC techinque is utilized to obtain samples from the posterior distribution which was im-plemented via WinBUGS. We then apply the Bayesian Deviance Information Criteria (DIC)to select the best model for real data from ball bearing failures where information regardingprevious failures are available. The credible interval is used to check the significance of theparameters of the selected model. We also used the posteriorpredictive distribution for modelchecking by comparing the observed and posterior predictive mean number of failures
