Estimation of Reliability for Exponential Distributions Using Ranked Set Sampling with Unequal Samples

This paper considers the problem of estimating the reliability R = P(X > Y) for a system with strength X and stress Y . We present the best linear unbiased estimator and the modified maximum likelihood estimator based on ranked set sampling with unequal samples, when X and Y both follow exponential distributions. The properties of these estimators are investigated. The proposed estimators are shown to be superior to the known estimators based on simple random sampling and ranked set sampling. Finally, results of an application to a real data set are presented to illustrate some of the theoretical findings.