A stochastic hybrid systems model of common-cause failures of degrading components

Abstract

Common-Cause Failures (CCFs) are an important threat to safety critical systems. Most existing CCF models assume that the component failure behavior does not vary over time. Such an assumption is often challenged in practice due to the influence of various degradation mechanisms, e.g., wear, corrosion, fatigue, etc. In this paper, we develop a new model for CCFs considering components degradation. The model is developed in the mathematical framework of Stochastic Hybrid Systems (SHS). The CCFs are modeled as random shock processes that affect a group of components simultaneously and the components degradation processes are modeled by stochastic differential equations derived from physics-of-failures. The benefit of using the SHS model for CCFs is that the developed model is analytically solvable. The system reliability can, then, also be solved analytically in closed form. The proposed CCF modelling framework is demonstrated by a numerical example of a three-unit redundant system and, then, applied to an Auxiliary Feedwater Pump (AFP) system of a Nuclear Power Plant (NPP). A comparison to the Binomial Failure Rate (BFR) model of literature shows that by considering the components degradation processes, the proposed model can accurately describe the CCF effect on the reliability of a system with degrading components.