Selection of the best minimal repair systems for Weibull lifetime distribution: A Bayesian approach

Abstract

The selection of the ‘best’ system and a subset of ‘best’ systems among k repairable systems () is considered, based on Bayesian and Empirical Bayes selection rules. ‘Best’ is determined in terms of highest reliability or lowest risk. The lifetimes of the systems are assumed to be Weibull distributed. The priors assigned to the Weibull distributions’ parameters are induced from standard priors used for the reliability and the hazard rate, i.e. the negative-log-gamma and the gamma, respectively. The component-wise Metropolis-Hastings algorithm is used for the computation of the Bayesian and Empirical Bayes selection rules. The proposed approaches are illustrated via a simulation study and applied on a classical data set of the literature.