Sensitivity analysis for fuzzy random reliability

Based on the basic definition of fuzzy random reliability sensitivity, the general numerical simulation method is presented for fuzzy random reliability sensitivity estimation. The variance and the variation coefficient are derived for the numerical estimation of the fuzzy random reliability sensitivity. In case that the fuzzy basic variables possess Gaussian membership functions, the fuzzy random reliability sensitivity can be transformed into the random reliability sensitivity, which can be well solved by the available methods. After the fuzzy random reliability sensitivity is transformed into the random one, the chain rule is employed to obtain the sensitivity of the fuzzy random failure probability with respect to the distribution parameters of the Gaussian membership function. For a symmetric triangle membership, a commonly used function in engineering) two fuzzy random reliability sensitivity methods are constructed on the basis of two equivalent transformations from the symmetric triangle membership to the Gaussian one respectively. One of them is named as 3σ criterion, the other is named as max.-min. method. Since the shape of the symmetric triangle membership function can be replaced by the max.-min. method more closely than by the 3σ criterion, the max.-min. method is more applicable to estimate the fuzzy random reliability sensitivity in case of the symmetric triangle membership, which is demonstrated by the given examples.