Bayesian Estimation Based on Sequential Order Statistics for Heterogeneous Baseline Gompertz Distributions

Tzong-Ru Tsai, Hua Xin and Chiun-How Kao
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Tzong-Ru Tsai: Department of Statistics, Tamkang University, Tamsui District, New Taipei City 251301, Taiwan
Hua Xin: School of Mathematics and Statistics, Northeast Petroleum University, Daqing 163318, China
Chiun-How Kao: Department of Statistics, Tamkang University, Tamsui District, New Taipei City 251301, Taiwan

Mathematics, 2021, vol. 9, issue 2, 1-21

Abstract: A composite dynamic system (CDS) is composed of multiple components. Each component failure can equally induce higher loading on the surviving components and, hence, enhances the hazard rate of each surviving component. The applications of CDS and the reliability evaluation of CDS has earned more attention in the recent two decades. Because the lifetime quality of components could be inconsistent, the lifetimes of components in the CDS is considered to follow heterogeneous baseline Gompertz distributions in this study. A power-trend hazard rate function is used in order to characterize the hazard rate of the CDS. In order to overcome the difficulty of obtaining reliable estimates of the parameters in the CDS model, the Bayesian estimation method utilizing a hybrid Gibbs sampling and Metropolis-Hasting algorithm to implement the Markov chain Monte Carlo approach is proposed for obtaining the Bayes estimators of the CDS parameters. An intensive simulation study is carried out to evaluate the performance of the proposed estimation method. The simulation results show that the proposed estimation method is reliable in providing reliability evaluation information for the CDS. An example regarding the service system of small electric carts is used for illustration.

Keywords: composite dynamic system; hazard rate; heterogeneity; Markov chain Monte Carlo; sequential order statistics (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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