A multi-stage resilience analysis framework of critical infrastructure systems based on component importance measures

•Proposed a new resilience metric, considering both technical and organizational resilience.•Optimized system resilience throughout multiple stages of the resilience process while considering the multi-state of system components.•Reformulated various importance measures based on the new resilience metrics, considering the effect of resilience management strategies on components’ state.•Introduced a components importance analysis framework aimed at determining the components importance ranking at different stages of the resilience process.•Presented a comprehensive importance-based framework for resilience analysis and optimization, considering the impact of multi-stage continuous dynamic organizational strategies on system resilience. Critical infrastructure systems (CISs) are large-scale and intricate systems that are the backbone of modern society. However, current CISs are exposed to various unpredictable disturbances, including terrorist attacks, cyber-attacks, and extreme hazards. Consequently, the issue of resilience, encompassing both assessment and strengthening, is increasingly coming to the fore. This study proposes an innovative framework for resilience analysis based on component importance measures. This framework evaluates the importance of affected components at different disturbance stages and optimizes system resilience. Initially, a new resilience metric is formulated, considering both technical and organizational aspects of CISs resilience. Following that, by integrating the new resilience metric with various importance measures and considering the multi-state of components, we comprehensively rank the importance of affected components throughout the resilience process. Resilience management strategies used to enhance CIS's resilience are, therefore, investigated. Finally, we demonstrate the framework's applicability by applying it to a power system. This comprehensive multi-stage importance-based resilience analysis framework can assist decision-makers in formulating proactive and continuous resilience strategies for handling unexpected events across design, operation, response, and recovery stages.