Multicomponent stress-strength reliability estimation for the standard two-sided power distribution

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Cetinkaya C., Genc A. İ.

HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS, vol.51, no.2, pp.587-605, 2022 (SCI-Expanded) identifier identifier identifier

  • Publication Type: Article / Article
  • Volume: 51 Issue: 2
  • Publication Date: 2022
  • Doi Number: 10.15672/hujms.936632
  • Journal Name: HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, zbMATH, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.587-605
  • Keywords: Bayesian estimation, maximum likelihood estimation, reliability, stress-strength model, two-sided power distribution
  • Çukurova University Affiliated: Yes

Abstract

A system of k components that functions as long as at least s components survive is termed as s-out-of-k:G system, where G refers to "good". In this study, we consider the s-outof-k:G system when X-1, X-2, ..., X-k are independent and identically distributed strength components and each component is exposed to common random stress Y when the underlying distributions all belong to the standard two-sided power distribution. The system is regarded as surviving only if at least s out of k (1 < s < k) strengths exceed the stress. The reliability of such a system is the surviving probability and is estimated by using the maximum likelihood and Bayesian approaches. Parametric and nonparametric boot-strap confidence intervals for the maximum likelihood estimates and the highest posterior density confidence intervals for Bayes estimates by using the Markov Chain Monte Carlo technique are obtained. A real data set is also analyzed to illustrate the performances of the estimators.