Improved point and interval estimation of the stress-strength reliability based on ranked set sampling

In this paper, the problem of estimating the stress-strength reliability (R) based on ranked set sampling (RSS) is studied in the exponential model. For estimation purposes, the preliminary test estimator and its shrinkage version as well as the Stein-type estimators of R are proposed. Their exact asymptotic distributional properties are derived. Conditions of superiority for the proposed shrinkage estimators are discussed. Furthermore, some improved bootstrap confidence intervals, based on the superior estimators, are constructed. An extensive simulation study is carried out in order to assess the inferential methods developed here. Both asymptotic and simulation evidences revealed that our proposed shrinkage strategies perform well in the estimation of R based on RSS. The results are concluded with the analysis of a real data set and a summary.