Human Reliability Dependency Assessment in Beyond Design-Basis Accidents: Extending the EMBRACE Dependency Equation

A dependency assessment is used to explicitly model causal relationships between two or more human events within an accident scenario and to estimate the conditional occurrence probability of subsequent human failures under the existence of antecedent human failures. This paper extends an existing dependency assessment method [empirical data-based crew reliability assessment and cognitive error analysis (EMBRACE)] for use in the human reliability analysis (HRA) of beyond design-basis accident (BDBA) scenarios requiring diverse and flexible coping strategies (FLEX).This work first identifies the key dependency mechanisms that are insufficiently represented in conventional internal event HRAs, including equipment inoperability and inaccessibility under extreme hazards; insufficiency of temporal, spatial, and manpower resources; changes in decision-making organizations; and additional performance shaping factor degradations. A generalized dependency equation is then proposed that augments the original EMBRACE formulation with new variables for equipment inoperability and inaccessibility, resource insufficiency, and decision-maker sameness, while preserving the existing terms for procedure transition similarity, cue recognition dependency, recovery factor, and additional contextual effect.Two case studies, namely, a storm-induced station blackout with direct current load shedding and FLEX power restoration, and a multi-unit earthquake scenario with portable generators, demonstrate how the extended equation quantitatively captures BDBA-specific dependencies and yields conditional human error probabilities that reflect resource sharing, cognitive coupling, and environmental constraints. The results indicate that the proposed framework improves traceability and realism in dependency quantification for FLEX-related human failure events and can support risk-informed decision making for severe external hazard scenarios. This work also highlights the need for further empirical data on BDBA-related human performance and organizational behaviors.