Classical and Bayesian estimation of reliability in a multicomponent stress-strength model based on the proportional reversed hazard rate mode

In this study, we consider a multicomponent system which has k statistically independent and identically distributed strength components X1,…,Xk and each component is exposed to a common random stress Y when the underlying distributions belonging to the proportional reversed hazard rate model. The system is regarded as operating only if at least s out of k(1≤s≤k) strength variables exceeds the random stress. The reliability of the system is estimated by using both frequentist and Bayesian approach. The Bayes estimates for the reliability of the system have been developed by using Lindley's approximation and the Markov Chain Monte Carlo method due to the lack of explicit forms. The uniformly minimum variance unbiased and exact Bayes estimates for the reliability of the system are also obtained analytically when the common scale parameter is known. The asymptotic confidence interval and coverage probabilities are derived based on both the Fisher and the observed information matrices. The highest probability density credible interval is constructed by using Markov Chain Monte Carlo method. Monte Carlo simulations are performed to compare the performances of the proposed reliability estimators. Real data set is also analyzed for an illustration of the findings.