Improved estimators for stress-strength reliability using record ranked set sampling scheme

In this paper, the problem of estimating the stress-strength reliability based on upper record ranked set sampling is studied. In the exponential parent distribution, improved estimation strategies including the preliminary test estimator (PTE) and Stein-type shrinkage estimator (SE) are developed using the maximum likelihood estimator (MLE) and a prior information about R. Next, asymptotic distributional properties of the proposed estimator are exactly derived. Then we compare the proposed estimators in terms of asymptotic relative efficiency criteria. Furthermore, we construct some bootstrap confidence intervals (CI) in order to achieve more accurate inferences. The results show that our proposed improved estimators are superior to the MLE in wide range of parameter space. Specifically, the proposed shrinkage preliminary test estimator (SPTE) outperforms the MLE uniformity for small values of type one error. Performance analysis is also investigated through some numerical endeavors.