Statistical Inference of Stress–Strength Reliability of a Parallel System with Mixed Standby Components

Abstract

This paper presents the Bayesian analysis of the stress–strength reliability of a parallel system with active and mixed standby components. The Bayesian estimators of the parameters of exponential and Weibull stress–strength distributions are obtained by assuming informative and noninformative prior for the parameters of the respective distributions. The Gibbs sampling procedure is used to compute the Bayesian stress–strength reliability. The asymptotic distributions, of the maximum likelihood estimators of the parameters of the corresponding distributions, and of the respective system reliabilities are presented. The bootstrap estimate and confidence interval are also obtained. The procedures are illustrated based on certain datasets.