【摘要】 《工程软设计理论》和《工程结构及系统的模糊可靠性分析》中将两个随机事件交集运算和并集运算的概率分为3种情况(完全相关、相互独立和存在一定的相关性),对应有不同的计算模型。实际上,完全相关和相互独立是存在一定相关性的特殊情况。从理论上讲,限制相关参数γ∈(0,1)的哈马邱尔算子作为考虑相关性时系统可靠度和失效概率的计算模型,当相关参数γ分别趋于0和1极限时,其极限也应分别趋于完全相关和相互独立的计算模型。然而,限制相关参数的哈马邱尔算子仅满足当相关参数趋于1时,其极限趋于相互独立的计算模型,而当相关参数趋于0时,其极限并不趋于完全相关的计算模型。针对这种情况,使用加差值的方法改进哈马邱尔算子,使之能适用于上述提到的三种情况。讨论改进的哈马邱尔算子的基本性质,分析改进的哈马邱尔算子存在的问题,并给出解决办法。算例的结果验证改进的哈马邱尔算子适用于组成系统的各单元完全相关的情形。更多还原

【Abstract】 Supposing the probability of intersection operation and union operation about two random events is calculated on the base of the relation that both events are completely dependent or mutually independent or to some extent dependent, the corresponding computation models are given in Theory of Soft Design in Engineering and Fuzzy Reliability Analysis of Engineering Structures and Systems. Actually, complete dependence and mutual independence of variables are extreme cases of variables having dependence of some degree. Theoretically, when Hamacher operator whose dependent parameter γ is bounded in the open interval(0,1) serves as the computation model for the analysis of systematic reliability considering failure dependence, the limit of Hamacher operator as γ→0,1 should respectively be equal to the computation model for complete dependence and mutual independence of two variables. Actually, the limit of Hamacher operator as γ→1 is equal to the computation model for mutual independence of two variables, and yet the limit of Hamacher operator as γ→0 is not equal to the computation model for complete dependence of two variables, so Hamacher operator is modified by the method of adding increment to Hamacher operator. The basic properties of the modified Hamacher operator are discussed in detail. The problem that modification of Hamacher operator brings is analysed, and the corresponding measures are taken. It is verified that the modified Hamacher operator is fit for the three forementioned cases by example.更多还原