###### Abstract  
As cyber threats continue to grow in complexity and persistence, resilience has become a critical requirement for cyber-physical systems (CPSs). Resilience quantitative assessment is essential for supporting secure system design and ensuring reliable operation. Although various methods have been proposed for evaluating CPS resilience, major challenges remain in accurately modeling the interaction between cyber and physical domains and in providing structured guidance for resilience-oriented design. This study proposes an integrated CPS resilience assessment framework that combines cyber-layer anomaly modeling based on Markov chains with mathematical modeling of performance degradation and recovery in the physical domain. The framework establishes a structured evaluation process through parameter normalization and cyber-physical coupling, enabling the generation of resilience curves that clearly represent system performance changes under adverse conditions. A case study involving an industrial controller equipped with a diversity-redundancy architecture is conducted to demonstrate the applicability of the proposed method. Modeling and simulation results indicate that the framework effectively reveals key resilience characteristics and supports performance-informed design optimization. c 2025 15 8285 10 June 2025 11 July 2025 11 July 2025 10 June 20  
in the context of cyber-physical systems (CPSs) that support critical infrastructures such as power grids, industrial control systems (ICSs), and transportation networks [2]. As CPSs become increasingly interconnected and vulnerable to sophisticated threats, resilience has shifted from being a desirable property to a fundamental requirement for ensuring system dependability and mission assurance [3]. In CPSs, resilience must be considered holistically across both the physical and cyber domains. Physical components, such as sensors and actuators, interact closely with cyber elements, including communication protocols, data links, and control algorithms. These interactions create tightly coupled dependencies, so cyber disruptions--whether caused by malicious attacks or accidental faults--can propagate into the physical domain, affecting system performance and safety [4]. To support robust system design and operational planning, it is essential to develop rigorous methods for quantifying CPS resilience in the face of such disruptions. Despite the growing consensus on the critical importance of cyber resilience in CPSs, significant challenges remain in quantitatively evaluating resilience and designing CPSs that are resilient by construction. These challenges arise from several core issues. From an evaluation perspective, resilience is a system-level property that lacks a unified definition and is often described too broadly, making it difficult to measure consistently [5]. From a design perspective, strategies to achieve resilience--such as redundancy, fault tolerance, adaptive control, and cyber defense--are diverse and hard to integrate within a single framework [6]. In CPSs specifically, the added complexity of cyber-physical coupling introduces a third challenge: the lack of an integrated modeling strategy for representing resilience processes across both the cyber and physical domains [7].