Abstract
Many real-world systems exhibit probabilistic functional dependence behaviour, where operations of some system components (dependent components) depend on function of another component (trigger component) in a probabilistic manner. A trigger component failure may cause two-fold effects. On one hand, if it occurs first, the corresponding dependent components may be isolated with certain probabilities, and such isolation effects can prevent system function from being compromised by further failures of those dependent components. On the other hand, if any of the dependent components experiences a propagated failure that occurs before the trigger component failure, the entire system can fail due to the propagation effect. This paper models such competitions between probabilistic failure isolation and failure propagation effects in reliability analysis of non-repairable systems through a combinatorial methodology. As demonstrated through examples, the method is applicable to arbitrary component time-to-failure distributions, and can handle diverse statistical relationships between component local and propagated failures.