Abstract
Considering the impact of the heterogeneous conditions of the mixture baseline distribution on the parameter estimation of a composite dynamical system (CDS), we propose an approach to infer the model parameters and baseline survival function of CDS using the maximum likelihood estimation and Bayesian estimation methods. The power-trend hazard rate function and Burr type XII mixture distribution as the baseline distribution are used to characterize the changes of the residual lifetime distribution of surviving components. The Markov chain Monte Carlo approach via using a new Metropolis–Hastings within the Gibbs sampling algorithm is proposed to overcome the computation complexity when obtaining the Bayes estimates of model parameters. A numerical example is generated from the proposed CDS to analyze the proposed procedure. Monte Carlo simulations are conducted to investigate the performance of the proposed methods, and results show that the proposed Bayesian estimation method outperforms the maximum likelihood estimation method to obtain reliable estimates of the model parameters and baseline survival function in terms of the bias and mean square error.
Highlights
The components in a n-component composite system often fail sequentially when the system is on duty continuously until the system is declared as a failure system
In order to overcome the computation complexity when obtaining the Bayes estimates of model parameters, the Markov chain Monte Carlo (MCMC) approach is used for Bayesian estimation, and we propose a new M-H within the Gibbs sampling (GS) algorithm to implement the MCMC approach
We proposed a maximum likelihood estimation method and a Bayesian estimation procedure using the MH-GS MCMC approach to obtain reliable Bayes estimators of the composite dynamical system (CDS) model parameters and baseline survival function based on sequential order statistics (SOSs) samples when the component lifetimes follow the baseline of mixture-Burr type-XII distribution (BXIID)
Summary
The components in a n-component composite system often fail sequentially when the system is on duty continuously until the system is declared as a failure system. An ncomponent composite system is an n-component composite dynamical system (CDS) if the failure of a component induces higher work loading on the surviving components of system. The lifespan of a CDS is usually defined as the r th (r ≤ n)-ordered component failure time due to the system structure designed or efficiency concerned. Because each component failure can induce higher loading on the surviving components, the risk of the system is increased along with the increase of the number of failure components. One working assumption for characterizing the increased risk of the CDS is to assume that all surviving components in the system can share the loading of stress. The observed ordered component failure times from the CDS system of equal load-share are called sequential order statistics (SOSs). Burr type-XII distribution, mixture-BXIID cumulative density function composite dynamical system equal-tailed credible interval generalized order statistic
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