Bayesian Estimation of the Parameters, Reliability and Hazard Rate Functions of Mixtures Under Accelerated Life Tests

Suppose that the lifetimes of the first r i items to fail in a random sample of size n i (type-II censoring) at stress v i , , are distributed according to a finite mixture model. The components of the model may represent different causes of failure and include, among others, the Weibull, compound Weibull, Pareto, power function, Gompertz and compound Gompertz distributions. In this paper, the Bayes estimates of the parameters, reliability and hazard rate functions are computed by using an approximate form due to Tierney and Kadane [Tierney, L., Kadane, J. B. (1986). Accurate approximations for posterior moments and marginal densities. J. Am. Statist. Assoc. 81:82–86]. A special attention is paid to a mixture of two Weibull components where the mean squared errors of the Bayes estimators are compared with their maximum likelihood counterparts via a simulation study.