相关性失效k/n(G)系统结构函数-可靠度计算的等效映射表征

Equivalent Mapping Characterization of Structure Function-Reliability Calculation for k/n(G) Systems Involving Failure Correlation

以全概率分解、递推法、结合幂等律运算给出并验证了k/n(G)系统结构函数-可靠度计算的映射表征,从而构成两者等效条件。引入Copula函数的相关理论,分别建立零部件相关性失效的同型、非同型单元k/n(G)系统可靠度预计模型,借助于结构函数-可靠度计算的映射表征,给出相关性失效k/n(G)系统一般性结构函数解析式,进而完成相应的结构重要度、失效灵敏度等应用分析。

With total probability decomposition, recursive method and idempotent law, the equivalent mapping characterization of structure function-reliability calculation for k/n（G） systems were derived and proved, so as to be equivalent condition to each other. By the utilization of Copula theory, the reliability calculation models for k/n（G） systems composed of the same type units and the unusual type units involving failure correlation of components were established respectively. By means of the mapping characterization of structure function-reliability calculation, the general analytical expression for k/n（G） systems with failure correlation was also presented. Finally, had a practical analysis of structure importance and failure sensitivity for the components in a special system.