Line sampling algorithm for fuzzy reliability sensitivity analysis

According to the definition of fuzzy failure probability for fuzzy failure domain, the methods of Fuzzy Reliability Sensitivity (FRS) analysis are presented. For linear performance function with independent normal variables and normal membership, an analytical method is derived for FRS analysis. In general case, the Monte Carlo numerical simulation method is presented to analyze the FRS. The evaluation of the FRS by the numerical simulation converges almost surely to the real value as the number of simulation approaches infinity. However its efficiency is low, especially for high dimensionality and small failure probability problems. To solve the disadvantage of the numerical simulation, line sampling algorithm is developed for the FRS analysis. By discretizing the integral region of the fuzzy failure probability calculation, the relationship between the FRS and the Random Reliability Sensitivity (RRS) is constructed, then the line sampling algorithm for the RRS is extended to the analysis of the FRS. The basic concept, the formulae and the implementation of this method for the FRS 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 the given examples.