Modeling the Interdependent Coupling of Safety and Security for Connected and Automated Vehicles: A Copula-Based Integrated Risk Analysis Approach

Safety and security are critical to the reliable operation of connected and automated vehicles (CAVs). While existing research has identified correlations between the two domains, a theoretical framework to analyze their interaction mechanisms and guide co-design remains lacking. To address this gap, this paper proposes a copula-based joint safety-security analysis method to quantify their coupling effects. First, we formulate time-varying cyberattacks using dynamic risk functions derived from survival analysis, while modeling random hardware failures with the Weibull distribution, as per the automotive industry standard ISO 26262. Second, to capture the dependence between functional safety failures and cyber threats, we introduce a joint failure model based on copula theory, employing both elliptical (e.g., Gaussian) and Archimedean (e.g., Frank) copula families to construct a system-level failure function. Furthermore, we provide formal theoretical analysis of the dependence structure in the safety-security coupling, yielding three key insights: (1) a monotonic relationship between joint failure probability and dependence parameters, (2) the mechanisms of defensive response mechanisms (such as patch deployment) in mitigating joint failures, and (3) quantifying the dynamic coupling strength between safety and security under dependence structures. Through comprehensive simulations, we evaluate the sensitivity of the joint failure behavior to three critical factors: copula dependence parameters, security patch deployment timing, and Weibull distribution parameters. Our dynamic failure model further illustrates how cyberattacks affect safety failures and, conversely, how functional faults affect security failures under dependencies structures. This study provides a quantifiable theoretical foundation for the co-design of safety and security in CAVs.