第46卷第4期 机械工程学报 Vol.46 No.4 2010年2月 JOURNAL OF MECHANICAL ENGINEERING Feb.2010 D0I:10.3901/JME.2010.04.150 研制阶段系统可靠性增长的Bayesian评估与预测 明志茂1张云安1陶俊勇12陈循1 (1.国防科技大学机电工程与自动化学院长沙410073； 2.马里兰大学可靠性与风险性研究中心马里兰州20742美国) 摘要：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先验分布容易定址和衡址先验参数确定的 方法，解决了超参数物理意义不明确难以确定问题。通过变量薛换的G6bs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侦测，扩展了 模型应用范闱。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。 关键词：可靠性增长模型Bayesian新Dirichlet分布与尔科夫蒙特卡罗模拟Gibbs抽样 中图分类号：TB114.3 Bayesian Reliability Assessment and Prediction During Product Development MING Zhimao ZHANG Yunan'TAO Junyong"2 CHEN Xun! (1.College of Mechatronics Engineering and Automation, National University of Defense Technology,Changsha 410073; 2.Center for Risk and Reliability,University of Maryland,MD 20742,USA) 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:Reliability growth model Bayesian analysis New Dirichlet distribution Markov chain Monte Carlo(MCMC)simulation Gibbs sampling 性能H趋先进，结构精密复杂，具有“小了样、高 前言 0 可靠性”的特点。其研制和生产都是分阶段、分批 次进行的，问时每一阶段或批次的试验次数又很少， 随着科学技术发展，现代武器装备的战术技术 并且每一阶段的试验信息并非服从同一总体。如何 充分利用不同阶段试验信息对产品的最终性能作出 国家部委顺研(51319030302)和1W家部委预研基金(9140A19030506 科学客观的评价就是异总体统计问题。 KG0166)愤助项日.20090319收到制稿，20090902收缘政稿 万方数据第46卷第4期 20l 0年2月 机械工程学报 JOURNAL OF MECHANICAL ENGINEERING V01．46 NO．4 Feb． 20lO DoI：10．3901／JME．2010．04．150 研制阶段系统可靠性增长的Bayesian评估与预测芈 明志茂1 张云安1 陶俊勇1，2 陈 循1 (1．国防科技大学机电工程与自动化学院长沙410073； 2．马里兰大学可靠性与风险性研究中心马里兰州20742美国) 摘要：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：’前阶段和后 续试验阶段，扣品可靠性的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H月确，简单易{r，利于工程应用。 关键词；可靠性增长模型Bayesian新Dirichlet分布 屿尔科夫蒙特卡罗模拟Gibbs抽样 中图分类号：TBl 14．3 Bayesian Reliability Assessment and Prediction During Product Development MING Zhima01 ZHANG Yunanl TAO Junyon91·2 CHEN Xunl (1．College of Mechatronics Engineering and Automation， National University ofDefense Technology,Changsha 410073； 2．Center for Risk and Reliability,University of Maryland，MD 20742，USA) 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 ofa weapon，a Bayesian reliability growth model is presented based 011 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 howto veriry 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 ofthe model．The analysis result of practical Cases shows that the parameters ofthe Bayesian model have clear and definite meaning and are convenient to use for engineering applications． Key words：Reliability growth model Bayesian analysis New Dirichlet distribution‘ Markov chain Monte Carlo(MCMC)simulation Gibbs sampling 0前言 随着科学技术发展，现代武器装备的战术技术 ’国家部蚕颅司f(51319030302)glIl4家部委预研基金(9140A19030506- KG0166)资助项目。20090319收到考U稿，20090902收纠修改稿 性能H趋先进，结构精密复杂，具有“小了样、高 可靠性”的特点。其研制和生产都是分阶段、分批 次进行的，同时每一阶段或批次的试验次数又很少， 并且每一阶段的试验信息并非服从同一总体。如何 充分利用不同阶段试验信息对产品的最终性能作出 科学客观的评价就是异总体统计问题。 万方数据