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Critical infrastructures are vital in supporting the essential services of society. However, they are susceptible to damage when confronted with disruptive events like earthquakes. This fosters a pressing demand for research geared towards building a resilient critical infrastructure. To furnish crucial benchmarks for enhancing system resilience, we developed a framework for assessing the resilience of critical infrastructures, considering their intricate multi-component configurations. Our framework conceptualizes overall resilience as a synthesis of four principal attributes: resistant, absorption, adaptive, and recovery resilience. Aiming at quantifying these attributes, the temporal performance behavior of the system is modeled via Markov processes. On this basis, resilience measures are defined concerning attributes within the framework, each incorporating both inherent and acquired aspects. The calculation formulas for these measures are derived analytically based on aggregated stochastic processes. This investigation also proves that, within the proposed framework, series systems are no more resilient than parallel systems. A case study of a potable water system subject to earthquakes is showcased to exemplify the devised assessment framework and calculation method. Meanwhile, some managerial insights are provided to designers and managers responsible for critical infrastructures. Managerial Relevance Statement–This article introduces a framework for assessing the resilience of critical infrastructures (CIs) in response to disruptive events. The findings indicate a progressive decline in both the inherent resistant and absorption resilience of CIs with increased operational duration, leading inevitably to interruptions. This highlights the imperative for CI designers to focus on enhancing inherent adaptive and recovery capabilities of CIs to counter such interruptions. Meanwhile, the study finds that both the acquired adaptive and recovery resilience initially increase before diminishing over the lifespan of CIs. This insight offers guidance for managers aiming to prolong the operational lifespan of CIs, emphasizing initial resource allocation to prevent potential interruptions, and recommending subsequent resource reallocation to facilitate rapid recovery from such interruptions. In addition, the research proves that parallel systems exhibit superior resilience compared to series systems, given identical components. This suggests a significant variance in the improvement level of systems with different structures when equivalent recovery resources are applied, underscoring the strategic importance of structural considerations in resilience enhancement efforts.

Failures of safety-critical mission-based systems, such as aircraft and submarines, could result in significant losses and damage. To enhance the survivability of such systems, their missions may be aborted if the failure risk becomes too high. We investigate such mission abort policies under a completely observed two-stage degradation process that progresses stochastically from “normal” to “defective” to “failure.” Mission abort decisions are considered as a function of the duration of the defective stage. This mission abort problem is formulated as a discrete-time optimal stopping problem with the goal of minimizing the expected total cost of mission failure and system failure. In addition to deriving some structural properties, we also numerically evaluate several intuitive heuristic policies. Finally, a joint optimization problem is formulated to simultaneously identify the optimal mission abort policy and the optimal investment to delay system deterioration.