Estimation of Stress-Strength Reliability for Weibull Distribution based on Type-II Right Censored Ranked Set Sampling Data

AKGÜL F. G., ŞENOĞLU B.

PAKISTAN JOURNAL OF STATISTICS AND OPERATION RESEARCH, vol.14, no.4, pp.781-806, 2018 (ESCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 14 Issue: 4
  • Publication Date: 2018
  • Doi Number: 10.18187/pjsor.v14i4.2239
  • Journal Name: PAKISTAN JOURNAL OF STATISTICS AND OPERATION RESEARCH
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus
  • Page Numbers: pp.781-806
  • Keywords: Stress-strength model, Ranked set sampling, Type-II right censoring, Modified maximum likelihood, Weibull distribution, Monte-Carlo simulation, UNBIASED ESTIMATION, THAN Y), LINDLEY, DESIGN
  • Karadeniz Technical University Affiliated: No

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.