Membership function of fuzzy reliability analysis by iteration based line sampling

For structures with random variables as well as fuzzy variables, a new iteration method based Line Sampling (LS) is presented for obtaining the membership function of fuzzy reliability. The value domain of the fuzzy variables is firstly obtained by means of the given membership level. Then the values of the fuzzy variables which make the performance function take extreme values are obtained by optimization modeling and iterating strategy, and the corresponding design points of the performance function in the reduced random variables space are also obtained at the same time. At last, based on the values of the fuzzy variables and the design points corresponding to the extreme values of the performance function, LS is employed to obtain the bounds of the reliability under the given membership level, and then the membership function of the fuzzy reliability is obtained. For the value domain of the fuzzy variables corresponding to each given membership level, the presented method considerably decreases computational effort by searching the extreme values of performance function instead of those of the reliability. Additionally, the design points corresponding to the extreme values of the performance function are guaranteed to converge to that corresponding to the extreme values of the reliability by the iterative strategy, and the reliability is obtained by LS, which improves the precision of the presented method. Several examples are used to illustrate the advantages of the presented method.