Bayesian Analysis For The Competing Risk Model

The competing risk model is commonly used in the reliability analysis. Due to the sophisticated internal structure and external working circumstance, many kinds of product may consist of serval physical or chemical causes of failure. Each of these causes is possible to result in the final failure. Although the idea of the accelerated life test on the competing risk product were raised by Nelson long time ago, it was not valued by the statisticians and the engineers at first, thus hindering the development of the research on this issue. Till now days, problems like the selection of the statistical method, the influence of the inter-dependence within different causes of failure and the manipulation of the mask data are still not completely solved and need further discussion.Based on Gibbs sampling, adaptive/rejection sampling and Metropolis method, Bayesian analysis for the competing risk model with multiple causes of failure is dis-cussed in this paper. Since the Bayesian method is able to involve the prior information of the product, especially that in the normal condition, it can help to improve the accu-racy of the result and the efficiency of the process in the inference, which makes up for the weakness of the traditional maximum likelihood method. Meanwhile, various skills of statistical calculation can also help to simplify the way of generating the posterior distribution if they are properly utilized.At the beginning of this paper, Weibull distribution, which is most widely used in the reliability statistics, is selected as the life distribution. And Bayesian inference on the Weibull competing risk model is conducted under the constant stress accelerated lift test. On this foundation, three-parameter Weibull distribution, Poly-Weilbull distribution, as well as the step stress condition are also included in the research.