Combinatorial Reliability Analysis of Imperfect Coverage Systems Subject to Functional Dependence

Functional dependence occurs when the failure of one component causes other components within the same system to become inaccessible or unusable. It is one of the dynamic behaviors that have been recognized in the dynamic fault tree analysis, where a dynamic gate called FDEP was designed to model such behavior. Traditional approaches to handling functional dependence in the reliability analysis of fault-tolerant systems with imperfect fault coverage are mainly based on Markov models, which are often computationally intensive, and even intractable due to the well-known state space explosion problem. In addition, the Markov-based approaches are typically restricted to exponential time-to-failure distributions for system components. In this paper, a combinatorial, separable method based on the divide-and-conquer paradigm and total probability theorem is proposed for addressing the above problems. The proposed method obviates the use of inefficient Markov models, offering exact, computationally-efficient solutions to the reliability analysis of imperfect coverage systems subject to functional dependencies. The proposed method is applicable to the analysis of large systems with any arbitrary time-to-failure distributions. Several case studies are given to illustrate the application and advantages of the proposed method.