A different sensitivity analysis for fuzzy random reliability with both fuzzy failure state and fuzzy safety state considered

For structure with fuzzy state and fuzzy variables, a general numerical simulation method is presented for fuzzy-random reliability sensitivity (F-RRS) estimation. In the case that fuzzy variables possess Gaussian membership functions, the F-RRS can directly be transformed into RRS, which can be easily solved by the available methods. For symmetric triangular membership functions, an equivalent transformation from the symmetric triangular membership functions to the Gaussian ones is established by the use of Minimum Least Squares (MLS). Details of what we have just written can be found in sections 1, 2 and 3 of the full paper. Section 4 gives three numerical examples, whose calculated results are presented respectively in Table 1(example 1), Table 2(example 2) and Table 4(example 3); in these tables, we compare our method with two existing ones and find that, in our opinion, our method qualifies to be applied to engineering problems, as an alternative to the two existing ones. For example 1, we present additional reliability sensitivity results in Figs. 1 through 7; the analysis of these results shows preliminarily that: (1) the effect of the fuzziness of state on failure probability is significant; (2) actually existing fuzziness cannot be neglected; otherwise dangerous evaluations may be obtained.