Abstract
Traditional approaches to handling functional dependence in systems with imperfect fault coverage are based on Markov models, which are inefficient due to the well-known state space explosion problem. Also, the Markov-based methods typically assume exponential time-to-failure distributions for the system components. In this paper we propose a new combinatorial approach to handling functional dependence in the reliability analysis of imperfect coverage systems. Based on the total probability theorem and the divide-and-conquer strategy, the approach separates the effects of functional dependence and imperfect fault coverage from the combinatorics of the system solution. The proposed approach is efficient, accurate, and has no limitation on the type of time-to-failure distributions for the system components. The application and advantages of the proposed approach are illustrated through analyses of two examples.