Inferences for stress–strength reliability of Burr Type X distributions based on ranked set sampling

Abstract

In this study, we consider the point and interval estimation of the stress–strength reliability based on ranked set sampling when the stress and the strength are both independent Burr Type X random variables. In the context of point estimation, we obtain the maximum likelihood (ML) estimator of using iterative methods. We also use Mehrotra and Nanda’s modified maximum likelihood methodology, which gives explicit estimator of as an alternative to the ML methodology. In view of interval estimation, we construct the asymptotic confidence interval of In addition, the bootstrap confidence intervals of are constructed based on two different resampling methods. The performance of the proposed estimators (both point and interval) is compared with their simple random sampling counterparts. A real data set from an agricultural experiment is analyzed to show the implementation of the proposed methodologies.