Combinatorial analysis of systems with competing failures subject to failure isolation and propagation effects

This paper considers the reliability analysis of binary-state systems, subject to propagated failures with global effect, and failure isolation phenomena. Propagated failures with global effect are common-cause failures originated from a component of a system/subsystem causing the failure of the entire system/subsystem. Failure isolation occurs when the failure of one component (referred to as a trigger component) causes other components (referred to as dependent components) within the same system to become isolated from the system. On the one hand, failure isolation makes the isolated dependent components unusable; on the other hand, it prevents the propagation of failures originated from those dependent components. However, the failure isolation effect does not exist if failures originated in the dependent components already propagate globally before the trigger component fails. In other words, there exists a competition in the time domain between the failure of the trigger component that causes failure isolation and propagated failures originated from the dependent components. This paper presents a combinatorial method for the reliability analysis of systems subject to such competing propagated failures and failure isolation effect. Based on the total probability theorem, the proposed method is analytical, exact, and has no limitation on the type of time-to-failure distributions for the system components. An illustrative example is given to demonstrate the basics and advantages of the proposed method.