Estimation of stress-strength reliability for weibull distribution based on type-II right censored ranked set sampling data

Abstract

In this paper, we consider the estimation of stress-strength reliability R = P (X < Y) under the type-II right censored data when the distributions of both the stress and the strength are Weibull. First, we discuss the estimation of R based on simple random sampling (SRS). Then, we use the effective and the efficient alternative of SRS which is known to be the ranked set sampling (RSS) to estimate R. In the estimation procedure of R, we use two different approaches they are i) maximum likelihood (ML) which requires an iterative method and ii) modified maximum likelihood (MML) which has an explicit form. Monte-Carlo simulation study is performed to identify the efficient sampling method (i.e., SRS or RSS) and the efficient estimation method (i.e., ML or MML). Finally, strength and wind speed data sets are analyzed to illustrate the proposed methods in practice.