Abstract
A combinatorial system reliability modeling method is proposed to consider the effects of correlated probabilistic competing failures caused by the probabilistic-functional-dependence (PFD) behavior. PFD exists in many real-world systems, such as sensor networks and computer systems, where functions of some system components (referred to as dependent components) rely on functions of other components (referred to as triggers) with certain probabilities. Competitions exist in the time domain between a trigger failure and propagated failures of corresponding dependent components, causing a twofold effect. On one hand, if the trigger failure happens first, an isolation effect can take place preventing the system function from being compromised by further dependent component failures. On the other hand, if any propagated failure of the dependent components happens before the trigger failure, the propagation effect takes place and can cause the entire system to fail. In addition, correlations may exist due to the shared trigger or dependent components, which make system reliability modeling more challenging. This paper models effects of correlated, probabilistic competing failures in reliability analysis of nonrepairable binary-state systems through a combinatorial procedure. The proposed method is demonstrated using a case study of a relay-assisted wireless body area network system in healthcare. Correctness of the method is verified using Monte-Carlo simulations.