AK-SESC: a novel reliability procedure based on the integration of active learning kriging and sequential space conversion method

•A new reliability method (AK-SESC), based on the combination of Active Learning Kriging with SESC, is proposed.•The efficiency of the sequential space conversion method (SESC) is Improved.•The capability of the proposed method was investigated with different examples.•The proposed method can deal with the problems with complexity and small value of failure probability.•The results indicate that the proposed method provides high accurate answers with much fewer function calls than SESC.