Line sampling algorithm for fuzzy reliability sensitivity analysis with correlative variables

According to the definition of fuzzy failure probability for fuzzy failure domain, the methods of fuzzy reliability sensitivity (FRS) analysis with correlative variables are presented. For linear performance function with normal variables and normal membership of the performance function to the fuzzy failure domain, an analytical method is derived for FRS analysis with correlative variables. For general engineering cases, a numerical simulation method is employed to perform the FRS analysis with correlative variables. Although numerical simulation method has wide applicability, its efficiency is low, especially for high dimensionality and small failure probability problems. To overcome the disadvantage of numerical simulation, a line sampling algorithm is developed for FRS analysis with correlative variables. By scattering the integral region of the fuzzy failure probability calculation, the relationship between the FRS and the random reliability sensitivity(RRS) with correlative variables is constructed, then the line sampling algorithm for the RRS is extended to the analysis of the FRS with correlative variables. The basic concept, the formulae and the implementation of the line sampling algorithm for the FRS with correlative variables are described in detail, and the advantages, such as high precision, high efficiency, and wide applicability for high dimensionality and small failure probability, are demonstrated by examples.