Redundancy Dependence in the Context of Competing Risks and Dynamic Degradation

Abstract

Parallel redundancy is a common approach to increase network availability. As a consequence of providing redundancy, the loading of that component changes, affecting its reliability. In this article, a holistic approach combining two models is introduced to assess both instantaneous and future effects on general failure rates in the context of competing risks and dynamic degradation. Concretely, both are designed to account for the duration of abnormal loading events. First, a per-unit-degradation method is introduced to map the different loading states onto a single normal operation sojourn time variable. Second, a time-inhomogeneous Markov chain is introduced to assess the irreversible degradation following a nondetrimental abnormal loading event. The numerical illustration shows that both models are necessary to correctly assess the effects of redundancy dependence if the underlying failure distribution has a shape parameter exceeding one.