Estimation of conditional stress strength reliability using ranked set sampling: exponential case

This study focuses on estimating conditional stress strength reliability of a system using ranked set sampling, when stress and strength variables follow independent exponential distributions. Two estimation methods are used, namely Maximum Likelihood Estimation (MLE) and bootstrap estimation. The asymptotic confidence interval is constructed based on a maximum likelihood estimator and the Boot-P confidence interval is constructed. A simulation study is carried out to determine the Mean Square Error (MSE) and length of the confidence interval. This study uses MSE and the length of the confidence interval to compare the estimator based on ranked set sampling to that based on simple random sampling in the context of exponential distribution.