An efficient algorithm for calculating Profust failure probability

For efficiently estimating the Profust failure probability based on probability input variables and fuzzy-state assumption, a General Performance Function (GPF) expression is established under the strict mathematical derivation for the Profust reliability model. By constructing the GPF, the calculation of the Profust failure probability can be transformed into the calculation of the traditional failure probability. Then various existing methods for the traditional failure probability can be used to estimate the Profust failure probability. Due to the high efficiency of the Adaptive Kriging (AK) model and the universality of the Monte Carlo Simulation (MCS), AK inserted MCS (abbreviated as AK-MCS) has been proven to be an efficient method for estimating the failure probability. Therefore, the AK-MCS combined with the GPF (abbreviated as AK-MCS + GPF) is proposed for estimating Profust failure probability. The proposed method greatly reduces the computational cost while ensuring the accuracy. Finally, four examples are given to validate the proposed AK-MCS + GPF. The results of the examples show the rationality and the efficiency of the proposed AK-MCS + GPF.