Resilience-based component importance measures

The resilience of critical infrastructures has become a major concern throughout the design, operation, and maintenance process in recent years. While traditional evaluation measures are mainly concerned with complete and timely restoration, this work considers simultaneously the cases where systems fail to recover thoroughly or timely. We define resilient limit and propose a new resilience evaluation framework for systems suffering different levels of breakdowns. Furthermore, from perspectives of topological structure, cold standby, and resilient limit of components, this paper proposes three resilience-based importance measures, namely, structure importance, redundancy importance, and reinforcement importance. Finally, we demonstrate our method with a numerical example, illustrating its effectiveness as a tool to evaluate the influences of component resilience characteristics on the overall system.