Estimation of P(X < Y) using ranked set sampling for the Weibull distribution

Akgul F. G., ŞENOĞLU B.

QUALITY TECHNOLOGY AND QUANTITATIVE MANAGEMENT, cilt.14, sa.3, ss.296-309, 2017 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 14 Sayı: 3
  • Basım Tarihi: 2017
  • Doi Numarası: 10.1080/16843703.2016.1226590
  • Dergi Adı: QUALITY TECHNOLOGY AND QUANTITATIVE MANAGEMENT
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.296-309
  • Anahtar Kelimeler: Stress-strength model, ranked set sampling, modified maximum likelihood, imperfect ranking, efficiency, Weibull, UNBIASED ESTIMATION, ORDER-STATISTICS, RELIABILITY, P(Y-LESS-THAN-X), PARAMETERS, SYSTEM
  • Karadeniz Teknik Üniversitesi Adresli: Hayır

Özet

This paper deals with making inferences regarding system reliability R = P(X < Y) when the distribution of the stress X and the strength Y are independent Weibull. In the literature, estimators based on simple random sampling (SRS) are widely used in estimating R. However, in recent years, ranked set sampling (RSS) has become popular in performing statistical inference. We, therefore, obtain the estimators of R based on RSS using maximum likelihood (ML) and modified maximum likelihood (MML) methodologies. The performances of the proposed estimators are compared with their counterparts based on SRS using Monte Carlo simulation. The simulation results show that the proposed estimators are more preferable than the estimators based on SRS in terms of efficiency. In addition, under the assumption of imperfect ranking the efficiencies of the ML and the MML estimators of R, based on RSS, are compared and the ML estimator of R is found to be more efficient. Finally, a real data-set is analysed to demonstrate the implementation of the proposed estimators at the end of the paper.