Resilience Analysis of k‐Out‐of‐n Systems

ABSTRACT This study proposes a resilience quantification framework tailored for ‐out‐of‐: systems, evaluating resilience across multiple dimensions, including resistant, absorption, response, recovery, adaptive, and overall resilience. By modeling system performance evolution using Markov processes, we develop resilience measures that incorporate both inherent and acquired aspects. The analytical formulas for resilience measures are derived according to aggregated stochastic processes, while the stochastic order theory is employed to establish the monotonicity of resilience with respect to and . A case study on a tsunami‐impacted offshore oil platform power system demonstrates the applicability of the proposed methods. The results emphasize the necessity of prioritizing recovery resilience in the design phase and leveraging past resilience cycles to develop adaptive learning strategies. Furthermore, this research offers potential approaches to bolster the resilience of critical offshore infrastructures, equipping decision‐makers with quantifiable strategies that consider both structural modifications and non‐adjustment scenarios.