###### Abstract
A variety of methods have been proposed to assess the cyber resilience of systems, as illustrated in Figure 1. These methods can be broadly categorized into four types: (1) static assessment metrics, such as availability, risk indexes, and reliability indicators, which provide high-level summaries but fail to capture dynamic system behavior; (2) red-teaming and adversarial simulation, which enable exploratory analysis and scenario testing, but often lack analytical generality and repeatability; (3) dynamic performance modeling, which focuses on time-dependent degradation and recovery in the physical domain, but frequently overlooks cyber-layer processes; and (4) cyber-layer security models, including attack graphs, stochastic processes, and game-theoretic approaches, which describe adversarial behaviors and defense mechanisms, typically in isolation from physical impacts. A detailed review of these approaches and their representative studies is provided in Section 2. Figure 1: Categories of cyber resilience assessment. While each of these methods contributes valuable insights, most either concentrate on a single domain or lack integration across the CPS architecture. A key missing element is a unified, mathematically grounded framework that accounts for both the dynamics of performance degradation and the stochastic nature of cyber faults or attacks. Such a framework should not only model temporal system behavior under adverse conditions but also support the design and validation of resilient system architectures. Addressing this gap forms the motivation of this paper. This study presents an integrated framework for evaluating cyber resilience in cyber-physical systems by combining dynamic performance modeling in the physical domain with probabilistic security modeling in the cyber layer. The approach bridges the gap between physical performance degradation and cyber-layer disruptions, enabling a unified and quantitative analysis of system-level resilience under adversarial conditions. The key contributions are as follows:  
* We develop a diversity-redundancy security architecture tailored to CPSs, incorporating heterogeneous execution units, voting mechanisms, fault isolation, and dynamic recovery. A Markov process model captures probabilistic transitions among cyber states--operational, degraded, detectable failure, and undetectable failure--under persistent threats. * We formulate a dynamic model that describes the system's functional evolution in response to cyber disturbances. This model quantifies resilience metrics such as degradation rate, recovery capacity, and long-term steady-state behavior. * We introduce a segmentation-weighted coupling method that aligns cyber-state sequences with corresponding physical performance phases. By weighting these segments according to their duration and stationary probabilities, the framework supports consistent and interpretable resilience evaluation. * A case study involving an ICS demonstrates the framework's effectiveness in comparing design alternatives and identifying critical resilience parameters. The remainder of this paper is organized as follows. Section 2 reviews related work on cyber resilience evaluation methods. Section 3 presents the proposed evaluation framework, including the security architecture, stochastic modeling, performance dynamics, and the cyber-physical coupling strategy. Section 4 provides a case study to validate the framework and demonstrate its practical value. Finally, Section 5 concludes this paper and discusses directions for future research.