基于Bayes变动统计理论的测试性外场统计验证方法

针对故障检测/隔离数据为"小子样"情况导致的测试性外场统计验证存在的周期长、验证结论置信度低等问题,研究并提出了基于Bayes变动统计理论的的测试性外场统计验证模型和方法。首先建立了不同寿命周期阶段故障检测率(FDR)的序化关系模型;然后以Dirichlet分布为先验分布,利用不同寿命周期阶段故障检测率先验估计值确定Dirichlet分布参数;在此基础上,融合"小子样、异总体"研制阶段增长试验数据和"小子样"外场使用数据,研究并提出了故障检测率的Bayes综合评估模型;引入Gibbs抽样方法求解故障检测率Bayes综合评估模型的复杂高维后验积分;最后在某机载稳定跟踪平台上开展了应用研究。结果表明本文方法能在较短的外场使用周期内,给出较高置信度的外场验证结论,为大型高可靠性装备测试性外场统计验证研究提供了重要的理论依据。

Research on Testability Field Statistics Verification Based on Bayes Inference Theory of Dynamic Population

For problems in the fault detection rate(FDR)field statistics verification test occurred when the field usage data for testability of equipment with high reliability is small sample,the Bayes inference on dynamic population-based FDR field statistics verification model and method are considered and launched.Firstly,an ordinal relation model of FDR at different stages is founded,a Bayes fusion method based on the Dirichlet prior distribution is studied,and a Bayes point estimation and the lower confidence limit on FDR in service are gained by fusing the expert experience,the test information at every stage and the field usage information.A method based on experts experience for determining the Dirichlet prior distribution parameters is given.Then,the Gibbs sampler is used to solve high dimensional integrals from which the posterior inference of FDR can be computed.Finally,The study demonstrates the FDR statistics verification by means of such model can produce the evaluation conclusion with high confidence level in a short field usage period and provide theory base for the research of field statistics verification for equipment with high reliability.