Stress-strength reliability estimation of a consecutive k-out-of-n system based on proportional hazard rate family

In this study, we consider point and interval estimations of stress-strength reliability in a consecutive k-out of-n system when the stress and strength variables follow the proportional hazard rate model. The reliability estimation is studied under both classical and Bayesian approaches when the scale parameter is unknown and known. The maximum likelihood and Bayes estimates of the reliability are derived. Bayes estimates are also obtained by using Lindley's approximation and Markov Chain Monte Carlo method when the exact forms cannot be obtained. Further, the uniformly minimum variance unbiased estimate of the reliability is derived when the scale parameters are known. Asymptotic confidence interval and the highest posterior density credible intervals are constructed. A Monte Carlo simulation study is carried out to compare the performances of proposed estimators. Two real data sets are analysed to show how the findings may work in practice.