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

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.

Parameter Estimation for Composite Dynamical Systems Based on Sequential Order Statistics from Burr Type XII Mixture Distribution

“…Because the current on the LED panel is unchanged, each LED failure will enhance the stress loading of each surviving LED until the LED panel malfunctions. Tsai et al [33] proposed a Bayesian estimation method to evaluate the reliability of the CDS with heterogeneity condition, and Tsai et al [34] proposed a Bayesian method and a profile maximum likelihood estimation method to infer the reliability of a video graphics array (VGA) when the adapters come from dual suppliers based on interval-censored samples. When dual suppliers support components for a CDS company simultaneously, using a mixture distribution is better than using a single distribution for characterizing the baseline component lifetimes for the study of CDS reliability.…”