基于模糊事件概率理论的模糊可靠性分析通用方法

讨论了从已知的模糊信息的隶属函数，确定模糊失效事件的隶属函数的方法，以便能利用模糊事件概率理论进行模糊可靠性分析，给出模糊可靠性分析通用而统一的方法；并给出了强度为几种常用模糊分布时，所确定的模糊失效事件的隶属函数的具体表达式，分析了模糊失效事件的隶属函数的曲线特性。由于获得的模糊失效事件的隶属函数的形式比较复杂，用模糊事件概率理论进行模糊可靠性分析时，不可能得到计算模糊失效事件概率的解析式，因此通过仿真所确定的模糊失效事件的隶属函数的数学期望的方法，估计模糊失效事件的发生概率。本文讨论的通过确定模糊事件的隶属函数，用模糊事件概率理论进行模糊可靠性分析的方法具有普遍意义。

A general approach for fuzzy reliability analysis based on the fuzzy probability theory

In the paper, an approach how to obtain membership function of fuzzy failure event from the known membership function of fuzzy information is discussed. Therefore, fuzzy reliability can be analyzed by utilizing the fuzzy probability theory, and the general and unified approach for analyzing fuzzy reliability is given. Also, concrete expressions of the determined membership function of the fuzzy failure event are given when strength is any one of common used fuzzy distributions, and the curve characteristic of the obtained membership function is analyzed. Because of the complexity of the obtained membership function, analytical formula for calculating probability of the fuzzy failure event cannot be obtained when fuzzy reliability is analyzed based on the fuzzy probability theory. For this reason, the probability of the fuzzy failure event is estimated by simulating expectation of the obtained membership function of the fuzzy failure event. The approach for analyzing fuzzy reliability discussed in the paper, which makes use of the fuzzy probability theory by determining the membership function of fuzzy event firstly, is of universal significance.