Risk Analysis of Socio‐Technical Systems With Safety Functions Using CS and CFE Methods

ABSTRACT Ensuring the safety of systems that incorporate electrical, electronic, and programmable electronic safety‐related functions requires quantitative evaluation of risk control and/or reduction performance, typically expressed as the Safety Integrity Level (SIL) defined in IEC 61508. However, existing probabilistic approaches have limited capability to represent modern safety architectures in which Safety Functions (SFs) consist of interdependent elements arranged in series, parallel, or heterogeneous redundant structures. Such configurations are increasingly common in contemporary safety‐critical applications, including autonomous driving systems and humanoid robotics. This paper proposes a unified analytical framework for evaluating the dependability characteristics of SFs and the risk metric of Hazardous Event Rate (HER) through two key abstractions: the Component Function Set (CS) and the Critical Functional Element (CFE). These concepts allow complex safety‐related systems to be represented using consistent failure and restoration characteristics across structural variations. The framework derives dangerous failure rates, effective restoration rates, and unavailabilities for series, parallel, and mixed configurations. HER is formulated by combining Markov modeling of demand and failure dynamics with transformation into an equivalent fault tree using irreversible Priority‐AND (PAND) logic, avoiding exponential growth in state‐space size. The proposed method provides exact or tight upper bounds for HER and clarifies how architecture, diagnostic capability, and demand characteristics influence hazard occurrence. An illustrative example demonstrates applicability to systems with non‐uniform redundancy and diagnostic coverage. The framework offers a practical analytical tool for architecture‐aware functional safety evaluation in modern safety‐critical systems.