多态系统电磁脉冲易损性概率置信下限的贝叶斯估计

Susceptibility Assessment of Multi-State System to EMP with Lower Confidence Limit of Probability Based on Bayesian Method

针对多态系统电磁脉冲易损性评估问题,提出了基于贝叶斯理论的多态系统电磁脉冲易损性概率置信下限估计方法。分别基于贝叶斯方法及经典统计方法,给出了多态系统电磁脉冲易损性概率置信下限及效应实验达到给定状态概率所需最小样本量的计算方法。通过算例,对文中提出的方法进行了验证和比较。在无信息先验条件下,贝叶斯方法与经典方法计算结果较为接近,概率置信下限和所需最小样本量的估计结果主要依赖于当前实验信息;当先验信息具有显著倾向时,若当前实验信息与先验信息一致,则基于贝叶斯方法计算的概率置信下限更加准确,且所需最小样本量明显少于经典统计方法的计算结果。

An assessment method of the lower confidence limit of probability based on Bayesian theory, which can be used in the susceptibility assessment of the electronic system to electromagnet ic pulse （EMP）, is proposed. According to the multi-state phenonmenon of the electronic system and the feature of its EMP effects, the derivations of full probability formula from multinomial and Dirichlet distribution are discussed. The lower confidence limit of each system state probability and the least number of trials with given probability can be determined by using the proposed method. A case demonstrates that, the differences between the results of the proposed method and the classical statistical method are not significant with the non-information prior. But when the prior information is strictly according to the sample information of current experiments, the accuracy of the estimation of each system state probability is improved and the requirement of the number of trials is reduced by the proposed method.