Resilience has emerged as a crucial concept for evaluating structural performance under disasters because of its ability to extend beyond traditional risk assessments, accounting for a system’s ability to minimize disruptions and maintain functionality during recovery. To facilitate the holistic understanding of resilience performance in structural systems, a system-reliability-based disaster resilience analysis framework was developed. The framework describes resilience using three criteria: reliability (β), redundancy (π), and recoverability (γ), and the system’s internal resilience is evaluated by inspecting the characteristics of reliability and redundancy for different possible progressive failure modes. However, the practical application of this framework has been limited to complex structures with numerous sub-components, as it becomes intractable to evaluate the performances for all possible initial disruption scenarios. To bridge the gap between the theory and practical use, especially for evaluating reliability and redundancy, this study centers on the idea that the computational burden can be substantially alleviated by focusing on initial disruption scenarios that are practically significant. To achieve this research goal, we propose three methods to efficiently eliminate insignificant scenarios: the sequential search method, the n-ball sampling method, and the surrogate model-based adaptive sampling algorithm. Three numerical examples, including buildings and a bridge, are introduced to prove the applicability and efficiency of the proposed approaches. The findings of this study are expected to offer practical solutions to the challenges of assessing resilience performance in complex structural systems.