A Bayes analysis of a competing risk model based on gamma and exponential failures

The paper proposes a competing risk model based on minimum of gamma and exponential failures where the former reflects aging with shape greater than unity and latter corresponds to accidental failures. The proposed model is analyzed in a Bayesian framework using proper but weak priors for the parameters. The analysis is done using Markov chain Monte Carlo simulation, in particular, the Gibbs sampler with intermediate Metropolis steps. Some usual characterizations of the proposed model are given for completeness. The proposed procedures are finally illustrated by means of a simulated data example involving both accidental and aging failures. The paper also considers model compatibility study using the ideas of predictive simulation and compares the proposed model with its components based on the simulated data set. A comparison with a similar model based on increasing hazard rate Weibull and exponential failures is also given. The results are found to be satisfactory.