To deal with evaluating small failure probabilities, AK–SESC: a novel approach integrating an active learning Kriging meta-model (AK-MCS) and the SESC, a sequential space conversion method, is suggested. The efficiency of the proposed approach relies on the advantages of the AK-MCS and its updating feature to evaluate the actual performance function and the superiority of SESC in estimating small failure probabilities. Although there are effective methods for small probabilities, the beauty of this approach is that it is derived from the probability integral with no simplifications while providing results of high accuracy. Different problems were solved to study the AK–SESC applicability. The main effort of this method is reducing the function call numbers of the original SESC while reaching the same accuracy as Monte Carlo Simulation (MCS). The reliability analysis results were compared with the main reliability methods of the Importance Sampling (IS), Subset Simulation (SubSim), Line Sampling (LS), First and also Second-Order Reliability Method (FORM and SORM). The solved problems indicate that the proposed approach provides accurate answers with much fewer function calls than SESC. So, it can be a promising method for reliability analyses involving nonlinear or high-dimensional performance functions with small failure probabilities.

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