基于Dirichlet先验分布的Bayes二项可靠性增长方法

Bayesian Method for Binomial Reliability Growth Based on the Dirichlet Prior Distribution

由于产品系统的复杂性和试验的高费用,并且产品的可靠性增长试验往往基于小样本,因此解决小样本问题在可靠性增长试验中也是非常重要的.借助Bayes理论,假设先验分布为Dirichlet分布,解决二项可靠性增长问题,能够充分借助先验分布和试验数据更合理估算出外场可靠性.同时在后验分布的计算上,利用Gibbs抽样的Markov Chain Monte Carlo(MCMC)方法仿真后验分布的计算.和传统的二项式Bayes方法进行比较,利用以Dirichlet分布为先验分布的Bayes方法非常适合阶段性可靠性增长试验评估,借助于专家的经验和以往类似产品的试验数据,容易定量和衡量先验参数.

Because of the complexity of product system and high costs for test of product, the reliability growth testing is based on small sample. It is important to research on solution of small sample in the reliability growth. Based on the Dirichlet prior distribution, Bayesian method for binomial reliability growth is studied. Through compared with conventional binomial Bayesian method, the method based on the Dirichlet prior distribution is more proper in the staggered reliability growth testing, it is easy to confirm the parameters of prior distribution by using the transcendental information, such as the experiences of experts and the testing data of similar product. Then the parameters of posterior distribution are calculated by using the simulation method of Markov-Chain Monte Carlo （MCMC）. At last, some examples are given.