Multistate System Reliability Modeling Using Copula Function

In this paper, Archimedean copula-based method was used to investigate the multi-state reliability analysis of a parallel system. First, the fundamental theory associated with Archimedean copula for both bi-variate and multivariate distributions as well as the tail dependence of Gumbel copula (an Archimedean copula family) were briefly introduced. Then, a general parallel system reliability problem was formulated for three identical components parallel system. Thereafter, the system reliability bounds of the parallel systems considered was derived using the copula approach. Graphical method was used to show failure space for the eight possible failure states associated with the system considered. Finally, an illustrative example is presented to demonstrate the proposed method. The results indicate that as the number of component failure increases, for parallel system with more than two components in parallel, the system probability of failure moves from the upper bound to the lower bound. Furthermore, Archimedean copula (Gumbel copula), which has been successfully used to model probability of failure for bivariate distribution, cannot successfully model the probability of failure for all possible failure state associated with more than two components parallel.