An efficient method for estimating fuzzy failure probability-based global fuzzy reliability sensitivity

The global fuzzy reliability sensitivity can measure the effect of input on fuzzy failure probability (FFP) through the expected difference between the unconditional FFP and the conditional one. Thus, an efficient method is proposed to estimate this sensitivity index. The proposed method includes two steps. First, the unconditional–conditional FFPs are equivalently transformed into the integrals of the unconditional–conditional failure probabilities (FPs) by an introduced variable related to the fuzzy state assumption. The unconditional–conditional FPs can be further expressed as the integrals of the unconditional–conditional probability density functions (PDFs) of the output. Secondly, the unconditional–conditional PDFs are solved using the maximum entropy theory constrained by the unconditional–conditional fractional moments. These fractional moments can be solved simultaneously through the multiplicative dimensional reduction using the same group of Gaussian quadrature points. The computational cost of the proposed method grows linearly with the dimensionality, and the computational efficiency is greatly improved.