指数分布下贝叶斯统计试验方案设计研究

Research on the Design of Bayesian Statistical Test Scheme under Exponential Distribution

研究了指数分布下经典统计试验方案和贝叶斯统计试验方案设计准则,指出了基于后验风险的贝叶斯统计试验方案设计准则的不足,提出了基于最大后验风险的贝叶斯统计试验方案设计准则,并得到了其共轭先验分布下的超参数解析式。在此基础上,给出了基于最大后验风险的贝叶斯统计试验方案设计解析表达式和区间估计方法,得到了零先验信息情况下的贝叶斯统计试验方案,并与经典统计试验方案进行了比较分析。结合实际指出了经典统计试验方案存在的不足,探讨分析了当前装备内外场可靠性水平表现不一致的可能原因,具有较大的工程应用价值。

The design criteria of classical statistical test scheme and Bayesian statistical test scheme under exponential distribution are studied,and the deficiency of Bayesian statistical test scheme design criterion based on posterior risk is pointed out.The design criterion of Bayesian statistical test scheme based on maximum posterior risk is proposed and the hyperparametric distribution is obtained.On this basis,the analytical expression and interval estimation method of Bayesian statistical test scheme design based on maximum posterior risk are given,and the Bayesian based on maximum posterior risk are given,and the Bayesian statistical test scheme with zero prior information is obtained,and it is compared with the classical statistical test scheme.The shortcomings of the classical statistics test scheme are pointed out in combination with the actual situation.The possible reasons for the in consistent performan of the internal and external reliability level of equipment are discussed and analyzed,which has great engineering application value.