Moment method for general failure probability with fuzzy failure state and fuzzy safety state

For general reliability analysis with fuzzy failure state and fuzzy safety state, moment method is proposed to calculate general failure probability. In the integral operation of the general failure probability, the integral region is scattered according to the value of performance function. In the scattered integral region, the membership function of the performance function to the fuzzy failure region keeps approximately constant, with which the calculation of the general failure probability is transformed into that of the random failure probability. After the transformation from the general failure probability to the random failure probability is completed, moment method is employed to obtain the general failure probability directly. The concept and the implementation of the proposed method are described step by step, and the results of a number of numerical and engineering examples show that the proposed method possesses high precision for low and medium dimension problems.