Stress–Strength Inference on the Multicomponent Model Based on Generalized Exponential Distributions under Type-I Hybrid Censoring

Tzong-Ru Tsai, Yuhlong Lio, Jyun-You Chiang () and Ya-Wen Chang
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Tzong-Ru Tsai: Department of Statistics, Tamkang University, Tamsui District, New Taipei City 251301, Taiwan
Yuhlong Lio: Department of Mathematical Sciences, University of South Dakota, Vermillion, SD 57069, USA
Jyun-You Chiang: School of Statistics, Southwestern University of Finance and Economics, Chengdu 610074, China
Ya-Wen Chang: Department of Statistics, Tamkang University, Tamsui District, New Taipei City 251301, Taiwan

Mathematics, 2023, vol. 11, issue 5, 1-17

Abstract: The stress–strength analysis is investigated for a multicomponent system, where all strength variables of components follow a generalized exponential distribution and are subject to the generalized exponential distributed stress. The estimation methods of the maximum likelihood and Bayesian are utilized to infer the system reliability. For the Bayesian estimation method, informative and non-informative priors combined with three loss functions are considered. Because the computational difficulty on working posteriors, the Markov chain Monte Carlo method is adopted to obtain the approximation of the reliability estimator posterior. In addition, the bootstrap method and highest probability density interval are used to obtain the reliability confidence intervals. The simulation study shows that the Bayes estimator with informative prior is superior to other competitors. Finally, two real examples are given to illustrate the proposed estimation methods.

Keywords: multicomponent stress–strength model; generalized exponential distribution; Bayesian method; Markov chain Monte Carlo method; highest probability density interval (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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