CAJ | 학술논문

基于新Dirichlet先验分布,建立一种适合小子样复杂系统异总体可靠性增长分析的Bayesian模型.充分利用先验信息和阶段试验信息,结合产品研制的试验数据,利用最优化方法研究新的Dirichlet先验分布容易定量和衡量先验参数确定的方法,解决了超参数物理意义不明确难以确定问题.通过变量替换的Gibbs抽样简化了后验推断,合理估算出当前阶段和后续试验阶段产品可靠性的Bayesian点估计和置信下限;结合试验数据,利用该模型实现了未来阶段可靠性的预测,扩展了模型应用范围.实例表明该模型参数含义清晰明确,简单易行,利于工程应用.
기우신Dirichlet선험분포,건립일충괄합소자양복잡계통이총체가고성증장분석적Bayesian모형.충분이용선험신식화계단시험신식,결합산품연제적시험수거,이용최우화방법연구신적Dirichlet선험분포용역정량화형량선험삼수학정적방법,해결료초삼수물리의의불명학난이학정문제.통과변량체환적Gibbs추양간화료후험추단,합리고산출당전계단화후속시험계단산품가고성적Bayesian점고계화치신하한;결합시험수거,이용해모형실현료미래계단가고성적예측,확전료모형응용범위.실례표명해모형삼수함의청석명학,간단역행,리우공정응용.
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.