Stress–strength reliability of a non-identical-component-strengths system based on upper record values from the family of Kumaraswamy generalized distributions. Issue 3 (4th May 2018)

• Record Type: Journal Article
• Authors: Rasethuntsa, Tau Raphael; Nadar, Mustafa
• Is Part Of: Statistics. Volume 52:Issue 3(2018)
• Page Start: 684
• Page End: 716
• Publication Date: 2018-05-04
• Subjects: Stress–strength reliability -- Kumaraswamy generalized distributions -- record values -- Bayes estimator -- UMVUE; 62F10 -- 62F15 -- 62N02; Mathematical statistics -- Periodicals; 519.505
• DOI: 10.1080/02331888.2018.1435661
• Languages: English
• ISSNs: 0233-1888

Abstract

ABSTRACT: In an attempt to produce more realistic stress–strength models, this article considers the estimation of stress–strength reliability in a multi-component system with non-identical component strengths based on upper record values from the family of Kumaraswamy generalized distributions. The maximum likelihood estimator of the reliability, its asymptotic distribution and asymptotic confidence intervals are constructed. Bayes estimates under symmetric squared error loss function using conjugate prior distributions are computed and corresponding highest probability density credible intervals are also constructed. In Bayesian estimation, Lindley approximation and the Markov Chain Monte Carlo method are employed due to lack of explicit forms. For the first time using records, the uniformly minimum variance unbiased estimator and the closed form of Bayes estimator using conjugate and non-informative priors are derived for a common and known shape parameter of the stress and strength variates distributions. Comparisons of the performance of the estimators are carried out using Monte Carlo simulations, the mean squared error, bias and coverage probabilities. Finally, a demonstration is presented on how the proposed model may be utilized in materials science and engineering with the analysis of high-strength steel fatigue life data.