LAUSR

Abstract In the model of R = P ( Y X ) , X and Y usually represent the strength of a system and stress applied to it. Then, R is the measure of system reliability. In this paper, Bayes estimation of R = P ( Y X ) is studied under the assumption that X and Y are independent Weibull random variables with arbitrary scale and shape parameters. We show here for the first time how to compute the Bayes estimates and credible intervals for R in that case. First, a closed form expression for R is derived. Prior distributions are assumed for Weibull parameters, and the posterior distribution is presented. Next, by proposing an universal sample-based method according to the Monte Carlo Markov Chain (MCMC) method, we draw samples and compute the Bayes estimates and credible intervals for R. Through Monte Carlo simulations and two real data examples, the proposed method is demonstrated to be robust and satisfactory.