基于层次Bayesian网络及后验风险准则的故障样本量确定方法

针对现有测试性验证方法对装备系统结构考虑不足，且在双方风险约束条件下所确定的故障样本量过大问题，提出一种基于层次Bayesian网络和后验风险准则的故障样本量确定方法。根据装备系统结构建立测试性验证方法的层次Bayesian网络模型，并以故障检测率作为Bayesian网络 的传递参数；提出Bayesian网络不确定性推理算法，充分融合各层次测试性先验信息，同时基于偏度-峰度检验的拟合分布选取方法推导出系统故障检测率联合先验分布；进一步结合系统成败型数据确定其后验分布，基于后验样本数据集和Bayes后验风险准则设计故障样本量确定算法，通过实例进行分析。结果表明，与经典验证方法、传统Bayesian方法相比，所提方法在相同双方指标约束下能有效降低样本量。

Method for Determining Fault Sample Size Based on Hierarchical Bayesian Network and Posterior Risk Criteria

The existing testability verification methods take insufficient account of the equipment system structure and need a large number of fault sample size under both-sides' risk constraints. A fault sample size determination method based on hierarchical Bayesian network and posterior risk criteria is proposed. A hierarchical Bayesian network model of testability verification method is established according to the structure of an equipment system. In hierarchical Bayesian network model, the failure detection rate is used as the transmission parameter of the Bayesian network. Bayesian network reasoning algorithm is proposed to fully fuse the priori information of each level, and the joint prior distribution of fault detection rates is deduced based on fitting distribution selection method for skewness-kurtosis test. The posterior distribution is determined with the binomial data of the system. A fault sample size determination algorithm is established based on the posterior sample data and Bayesian posterior risk criteria, and is validated by an example. Compared with the classical and traditional Bayesian verification methods, the proposed method can reduce the sample size effectively under the same both-sides' risk constraints.