Statistical inference of the stress-strength reliability and mean remaining strength of series system with cold standby redundancy at system and component levels

Abstract

In this study, we consider the stress-strength reliability and mean remaining strength of a series system with cold standby redundancy at the component and system levels. Classical and Bayesian approaches are studied in order to obtain the estimates when the underlying stress, strength and standby components follow the exponential distribution with different parameters. Bayes estimates are approximated by using Lindley's approximation and Markov Chain Monte Carlo methods. Asymptotic confidence intervals and highest probability density credible intervals are constructed. We perform Monte Carlo simulations to compare the performance of proposed estimates. A real data set is analyzed for the purpose of illustration.