基于Bayes理论的成败型装备鉴定试验风险分析  

Qualification test risk analysis of binomial equipment based on Bayes theory

作　　者：李大伟[1] 王国栋 李永哲 LI Dawei;WANG Guodong;LI Yongzhe(41st Division,Unit 91550 of the Chinese People's Liberation Amry,Dalian Liaoning 116023,China)

机构地区：[1]中国人民解放军91550部队41分队,辽宁大连116023

出　　处：《航空动力学报》2021年第1期157-166,共10页Journal of Aerospace Power

摘　　要：为了充分考核成败型装备的性能指标,合理确定鉴定试验统计方案,利用Bayes理论对试验风险进行了重点研究。在选取先验分布为Beta分布的条件下,给出了工程中常用两种风险(平均风险和后验风险)的表达式,并详细解释了两种风险的研究思路和适用范围。在此基础上,从鉴定试验可能出现的结果出发,建立了最大后验风险模型,给出了其相关性质,并对比后验风险、经典统计风险,说明了其保守性和适用性的优点,更能保护使用方的利益。利用数值分析,说明基于最大后验风险确定的试验统计方案符合工程认识,相对经典统计风险,其减少试验总数18%~63%,验证了方法的可行性。同时,通过分析三种风险与先验信息、区间估计的数值关系,对最大后验风险的性质进行了验证,说明其具有较好的推广性。The qualification test risk of binomial equipment was investigated by Bayes theory to assess the performance index and establish qualification test scheme. The Beta distribution was chosen as prior distribution. The expressions of average risk and posterior risk were given. The research ideas and applications of two kinds of risk were explained. On this basis, the max posterior risk model was developed through investigating the result of qualification test. The max. posterior risk’s properties were given. Compared with posterior risk and classical risk, it demonstrated the conservation and feasibility of max. posterior risk. So the consumer benefit was protected. The test statistics scheme based on max. posterior risk conformed to the engineering rule. The test number decreased by 18%-63%, compared with test statistics scheme based on classical risk. It also analyzed the number relation between three kinds of risk and prior information, interval estimation. The properties of max. posterior risk were demonstrated, showing its wide application.

关 键 词：鉴定试验 成败型装备 Bayes理论 平均风险 后验风险 

分 类 号：V267[航空宇航科学与技术—航空宇航制造工程] O213.2[理学—概率论与数理统计]