基于Copula函数的单冷贮备串联结构可靠性分析

Copula Function-based Reliability Analysis of a Series System with a Single Cold Standby Unit

传统的系统可靠性模型不能很好地反映子系统间性能相依性对整机可靠性的影响,需要忽略系统组合初始可靠度问题。以串联结构为研究对象,研究了具有多个相依工作子系统和一个冷贮备单元的系统可靠性及平均失效前时间(MTTF),应用Copula函数描述了工作子系统之间复杂的寿命相依性,基于条件概率理论,建立了具有初始可靠度和冷贮备的子系统相依的系统可靠性模型,并给出了系统的MTTF显式。以单冷贮备的两串联结构系统为例,基于Farlie-Gumbel-Morgenstern(FGM)Copula函数及边缘寿命指数分布函数,分析了子系统之间的工作相依程度对整机系统可靠性的影响,将系统可靠性表示成不同失效率的指数可靠性函数的线性组合,验证了该建模方法的有效性,为工程系统的可靠性设计和可靠性管理提供了理论依据。

The traditional reliability model cannot well reflect the effect of performance dependency of units on the reliability of systems and neglect the problems of initial composite reliability. Confining the system to series connection, the system reliability and mean time to failure （MTTF） of a series dependence system with multi-subsystems and one cold standby unit are studied. The Copula function is applied to describing the performance dependence among units, and the reliability models of dependence units with initial reliability and cold standby unit are inferred based on the theories of reliability statistics and conditional probability, the expression for the MTTF of the series system is also obtained. Based on the fact that Farlie-Gum- beI-Morgenstern （FGM） Copula function and marginal lifetime is exponential distribution, a system with two-dependent-unit in series and a single cold standby unit is taken as an example; the effect on the reliability of system because of the depend- ence degree is studied and the system reliability can be expressed as the linear combination of exponential reliability functions with different failure rates. The validity of the modeling method is verified and the presented method provides the theoretical basis for reliability design of system and management from a practical point of view.