关键词: Bayesian, Gibbs抽样, 可靠性增长模型, 马尔科夫蒙特卡罗模拟, 新Dirichlet分布

Abstract: A Bayesian reliability growth model of diverse populations based on the new Dirichlet prior distribution is studied. Aiming at some history and expert information during the development of a weapon, a Bayesian reliability growth model is presented based on the new Dirichlet distribution. Bayesian point assessment and confidence lower limit on product reliability at current stage are inputted by comprehensively making use of prior information and field test information at every stage. The method for determining prior distribution parameters is given by using the method, it is easy to confirm the parameters of prior distribution, it solves the problem of how to verify the hyper parameters of the new Dirichlet prior distribution in view of unclear physical meaning of these parameters. It solves the problem that the interference on parameters of Bayesian poster higher dimensions cannot be calculated indirectly. Then, the Gibbs sampling algorithm is used to compute the posterior inference. The Bayesian estimators and Bayesian lower bound are gained for the reliability of every stage. Furthermore, based on the test data, the model can be used to predict the product reliability, which extends the application range of the model. The analysis result of practical cases shows that the parameters of the Bayesian model have clear and definite meaning and are convenient to use for engineering applications.

Key words: Bayesian analysis, Gibbs sampling, Markov chain Monte Carlo(MCMC) simulation, New Dirichlet distribution, Reliability growth model