Reliability analysis of a parallel dependent system with a single cold standby unit

Abstract

Establishing reliability models for multi-component parallel systems, however, is still a challenge problem when considering the dependence of component failures. The traditional reliability models of engineering system neglect the problems of initial reliability and standby redundancy, and cannot well reflect the effect of performance dependence of sub-systems on the reliability of the system. In this paper, the reliability of a parallel system with active multi-components and a single cold standby unit is studied. The active components are dependent and the dependence is modelled by a copula function. Based on the theories of conditional probability, we obtained the explicit expressions for the reliability and the MTTF of the system by using the copula function and marginal lifetime distributions. Let the copula function be the FGM copula and the marginal lifetime distribution be exponential distribution, a system with two parallel dependent units and a single cold standby unit is taken as an example, the effect on the reliability of the system with dependence degree is studied, and the system reliability can be expressed as the linear combination of exponential reliability functions with different failure rates. Finally, an example is used to verify the effectiveness of the modelling method.