A new application of R = P[Y < X] for the inverse Lindley distribution using ranked set sampling

In this paper, we consider the problem of performing inference about reliability parameter R = P[Y < X] based on ranked set sampling (RSS) when the distribution of stress Y and strength X are inverse Lindley. The point estimator of R based on (RSS) using maximum likelihood method is obtained. In context of interval estimation an asymptotic confidence interval (ACI) and bootstrap confidence interval (BCI) are derived for R based on (RSS). The effectiveness of the proposed estimator is indicated in simulation study which compare the proposed estimators by their corresponding based on simple random sample (SRS). Finally a real data in medicine is used to illustrate our proposed estimators.