Reliability analysis method for structure with fuzzy variable

Based on the general numerical simulation of the fuzzy random failure probability estimation for structure with random and fuzzy basic variables, the variance and the variation coefficient are derived for the estimation of the fuzzy random failure probability. Since the calculation of failure probability of fuzzy random structure, where the fuzzy variables possess Gaussian membership functions, can be transformed into that of random structure, two approximate methods are introduced to transform the symmetric triangle membership function, a commonly used function in engineering, into the equivalent Gaussian one. One is named as ″3σ″ criterion method, the other is named as ″Max.-Min.″ method. The analysis of theory and the results of the examples shows that the shape of the symmetric triangle membership function can be replaced by the ″Max.-Min.″ method more closely than by the ″3σ″ criterion method, hence the ″Max.-Min.″ method is more applicable to estimate the fuzzy random failure probability when the fuzzy variables possess the symmetric triangle membership functions.