多阶段含延缓纠正可靠性增长的MS-NHPP模型及其Bayes分析

针对复杂航空机电系统的多阶段含延缓纠正可靠性增长试验,提出了多阶段非齐次泊松过程(MS-NHPP)模型及其Bayes分析方法。该模型将多个阶段试验看做多个非齐次泊松过程(NHPP),它们具有相同的时间起点和不同的强度函数参数,并满足序化约束关系。对该模型采用Bayes方法进行分析,以Dirichlet分布作为验前分布,并在验后计算中采用基于Metropolis-Hastings准则的马尔可夫链蒙特卡罗(MCMC)方法获得各阶段可靠性参数的验后期望、方差与置信限。实例分析表明,该方法可以有效融合多阶段可靠性增长试验数据以及专家经验和历史信息,尤其适用于小样本情况,参数估计值满足序化约束关系,可靠性增长评估结果更为可信。

MS-NHPP Model and Bayesian Analysis for Multistage Reliability Growth with Hybrid Fix Modes

For the multistage reliability growth tests with hybrid (instant and delayed) fix modes for complex aeronautic mechatronic systems, an multistage nonhomogeneous poisson process (MS-NHPP) model and its Bayesian analysis are presented. In the model, the multistage test is regarded as a combination of multiple nonhomogeneous poisson process (NHPP) processes with the same starting point but different intensity function parameters that satisfy some ordinal constraints. In the corresponding Bayesian analysis with prior Dirichlet distribution, the posterior expectations, variances and confidence limits of reliability parameters of all test stages are derived by Markov chain Monte Carlo (MCMC) sampling based on the Metropolis-Hastings principle. The example analysis indicates that this method can effectively integrate multistage test data, expertise and historical information with sound applicability to small sample cases, and that it can derive parameter estimates that satisfy ordinal constraints and obtain reliable evaluation results for reliability growth tests.