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 $R=P\left(X<Y\right)$ based on ranked set sampling when the stress $\mathrm{X}$ and the strength $\mathrm{Y}$ are both independent Burr Type X random variables. In the context of point estimation, we obtain the maximum likelihood (ML) estimator of $R$ using iterative methods. We also use Mehrotra and Nanda’s modified maximum likelihood methodology, which gives explicit estimator of $R$ as an alternative to the ML methodology. In view of interval estimation, we construct the asymptotic confidence interval of $R.$ In addition, the bootstrap confidence intervals of $R$ 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.

Keywords:

• Burr Type X distribution
• Efficiency
• Modified maximum likelihood
• Ranked set sampling
• Stress-strength reliability

MATHEMATICS SUBJECT CLASSIFICATION:

• 62F10
• 62F15
• 62N05