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Bayesian Inference of System Reliability for Multicomponent Stress-Strength Model under Marshall-Olkin Weibull Distribution
oleh: Liming Zhang, Ancha Xu, Liuting An, Min Li
Format: | Article |
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Diterbitkan: | MDPI AG 2022-10-01 |
Deskripsi
Industrial systems often have redundant structures for improving reliability and avoiding sudden failures, and a parallel system is one of the special redundant systems. In this paper, we consider the problem of reliability estimation for a parallel system when one stress variable is involved, which is called the multicomponent stress-strength model. The parallel system contains two components, and their joint lifetime follows a Marshall–Olkin bivariate Weibull distribution, while the stress variable is assumed to be the Weibull distribution. Due to the complicated form of the likelihood function, a data augmentation method is proposed, and then the Gibbs sampling algorithm is constructed to obtain the Bayesian estimation of the system reliability. The proposed method is evaluated by a simulated dataset and Monte Carlo simulation study. The simulation results show that the proposed method performs well in terms of relative bias, mean squared error and frequentist coverage probability.