基于新Dirichlet先验分布的指数寿命型产品多阶段可靠性增长Bayes分析

本文基于新的Dirichlet先验分布，建立了多阶段指数寿命型产品可靠性增长的Bayes模型。本模型充分利用先验信息和阶段试验信息，采用最优化方法解决了新的Dirichlet先验分布超参数因物理意义不明确而难以确定的问题；利用Gibbs抽样算法进行后验推断，合理估算出当前阶段和后续试验阶段产品可靠性的Bayes点估计和置信下限，并利用该模型研究实现了对产品可靠性的预测。实例证明了该模型在多阶段指数产品可靠性增怅分析中的直观性与有效性。

Multi-stage Reliability-Growth Bayes Analysis for Exponential Product Based on New Dirichlet Prior Distribution

A new method for the application of Bayes theory to the reliability-growth for exponential distribution was developed. Lismg some history and expert information during the development of a product, a Bayes reliability-growth model was presented based on new Dirichlet distribution. Bayes point estimation and lower confidence limits on product reliability at current stage were calculated by comprehensively making use of prior information and field test information at every stage. The method for determining prior distribution parameters was given by optimization which is easy to confirm the parameters of prior distribution, and to solve the problem of how to verify the hyper parameters of the new Dirichlet prior distribution because of these parameters having no specific physical meaning. The Oribbs sampling algorithm was used to solve the problem that interference on parameters of Bayes poster higher dimensions can’t be calculated directly, and numerical simulations were performed by the mod?el. The analyzed result of practical cases proves the observability and validity of the model.