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

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