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

作　　者：唐家银[1,2] 何平[1] 郑杰[1] 赵联文[1] 李裕奇[1] 

机构地区：[1]西南交通大学数学学院统计系,四川成都610031 [2]西南交通大学牵引动力国家重点实验室,四川成都610031

出　　处：《数理统计与管理》2014年第4期682-690,共9页Journal of Applied Statistics and Management

基　　金：教育部人文社会科学研究青年基金(11YJCZH154);中国铁路总公司科技研究开发计划项目(2013J006-B);四川省统计科学研究计划重点项目(2012sc050);国家自然科学基金(51205326);中央高校基本科研业务费专项资金(SWJTU12CX058;SWJTU12ZT14);四川省科技厅基础应用项目(2012JY0022)

摘　　要：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.

关 键 词：K/N(G)系统 结构函数 可靠度计算 失效相关性 COPULA 

分 类 号：TB114.3[理学—概率论与数理统计] O212[理学—数学]