摘要
为解决k/n(F)表决可修系统中零部件的故障相关干涉问题,根据零部件工作寿命之间的正相关结构,运用Copula函数的相关性理论,提出微时间差t→t+Δt内系统一步状态转移矩阵概念,建立了故障相关的表决可修系统可靠性模型.模型全面考虑了共因故障、零件工作寿命和修复时间分布的一般性,从而突破传统独立指数型可修系统可靠性模型的三类局限性.验证了k/n(F)可修系统相关性模型的通用性,给出了Copula模型选择和估计相关程度参数的方法.
To solve the problem of failures correlation interference in the components of k/n（F） repairable voting systems, a dynamic failure correlation interference models were de- rived based on the Copula theory and the negative correlation structure existed in lifetimes of components belonged to the same repairable system. In this presented model, the concept of one step state transition matrix for repairable systems in minimal time difference t → t ＋ t was given, and common cause failure, the general continuous distributions for working times and repair times were all took account, so it broke through the three types of limitations in traditional independent exponential reliability models. Furthermore, the generality of k/n（F） model was verified. The estimation methods for the correlation degree parameter and selection criterion for Copulas were given. An example showed that the feasibility and effectiveness of the theory.
出处
《数学的实践与认识》
CSCD
北大核心
2013年第1期108-117,共10页
Mathematics in Practice and Theory
基金
教育部人文社会科学研究青年基金(11YJCZH154)
国家自然科学基金(51175439)
中央高校基本科研业务费专项资金(SWJTU12CX058
SWJTU12ZT14)
四川省统计科学研究计划重点项目(2012sc050)
四川省科技厅基础应用项目(2012JY0022)
