In the field of the system reliability analysis with multiple failure modes, the advances mainly involve only random uncertainty. The upper bound of the system failure probability with multiple failure modes is usually employed to quantify the safety level under Random and Interval Hybrid Uncertainty (RI-HU). At present, there is a lack of an efficient and accurate method for estimating the upper bound of the system failure probability. This paper proposed an efficient Kriging model based on numerical simulation algorithm to solve the system reliability analysis under RI-HU. This method proposes a system learning function to train the system Kriging models of the system limit state surface. The convergent Kriging models are used to replace the limit state functions of the system multi-mode for identifying the state of the random sample. The proposed system learning function can adaptively select the failure mode contributing most to the system failure probability from the system and update its Kriging model. Thus, the efficiency of the Kriging training process can be improved by avoiding updating the Kriging models contributing less to estimating the system failure probability. The presented examples illustrate the superiority of the proposed method.
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