A generalized Subset Simulation approach for estimating small failure probabilities of multiple stochastic responses

•A generalized Subset Simulation is developed for multiple stochastic responses.•Unified intermediate events are constructed to solve the sorting difficulty.•The proposed approach is more efficient than the original Subset Simulation.•The proposed approach may be used in reliability-based optimization design. Estimating failure probabilities of multiple stochastic responses using a single run of Subset Simulation remains a challenging task in structural reliability analysis. To address this issue, this study develops a generalized Subset Simulation (GSS) approach, in which a unified intermediate event is defined to drive the simulation procedure progressively approaching multiple failure regions simultaneously. It bypasses the sorting difficulty arising from the multiple stochastic responses. The failure probabilities of multiple stochastic responses are obtained simultaneously by a single run of GSS. Finally, four representative examples are used to demonstrate the efficiency, accuracy and robustness of the proposed GSS approach.