Objective Bayesian analysis of accelerated competing failure models under Type-I censoring

This paper discusses the Bayesian inference of accelerated life tests (ALT) in the presence of competing failure causes. The time to failure due to a specific cause is described by a Weibull distribution. A two-stage approach is utilized to obtain the estimates of parameters in the model. We use the Bayesian method to estimate the parameters of the distribution of component lifetimes in the first stage, in which two noninformative priors (Jeffreys prior and reference prior) are derived in the case of ALT, and based on these two priors we present the Gibbs sampling procedures to obtain the posterior estimates of the parameters. Besides, to overcome the problem of improper posterior densities under some conditions, we modify the likelihood function to make the posterior densities proper. In the second stage, parameters in the accelerating function are obtained by least squares approach. A numerical example is given to show the effectiveness of the method and a real data from Nelson (1990) is analyzed.