System Reliability Analysis for Rare‐Failure Problems by Combining Adaptive Kriging and System Subset Simulation

ABSTRACT The high‐quality development of complex products is typically characterized by a low system failure probability. For rare‐failure system problems, the improved AK‐MCS method for system reliability (AK‐SYS) may incur expensive computational costs due to the large Monte Carlo simulation (MCS) candidate sample pool. In this study, the adaptive Kriging with system subset simulation (AK‐SYS‐SS) is proposed. Firstly, the Kriging‐based SYS‐SS method is developed. Its two core components, that is, the suggested conditional probability density function and failure probability estimation, are derived, respectively. Secondly, a multilevel convergence criterion is proposed, which focuses on the accuracy of the threshold sequence and the last‐level conditional failure probability. On this basis, a corresponding adaptive parallel learning strategy is designed, which can automatically adjust the number of parallel samples and prioritize the exploitation of high‐risk domains. Finally, the proposed method is validated through three numerical examples (including series, parallel, and complex bridge systems) and one engineering example. The results demonstrate that AK‐SYS‐SS can provide accurate results for rare‐failure system problems.