A Bayesian Approach to Parallel Stress-Strength Models

Abstract This work presents a Bayesian approach for estimating the reliability of a parallel multi-component system. It is assumed that the strengths of the components are independent random variables, which are subjected to a common stress with the same distribution. It is supposed that the failure times follow exponential and Weibull distributions, respectively. The Bayesian analysis is developed assuming a highly informative prior and a less informative prior distribution, respectively. A simulation based on certain data sets is used to study the performance of the Bayesian solutions. The solutions are computed by Markov Chain Monte Carlo (MCMC) methods. Finally, some observations are made in relation to the maximum likelihood method and some extensions are discussed.