Abstract: The general formulae of equivalent probability density function, equivalent mean value and equivalent standard deviation are given by means of the transformation from fuzzy variables to equivalent random variables.Specific formulae of equivalent mean value and equivalent standard deviation are obtained when the membership functions of the fuzzy variables are commonly used ones.Based on the formula of limit state, fuzzy reliability in complex cases is computed by the advanced first order second moment method in the convectional reliability theory, and the reliability index to measure fuzzy reliability is obtained.An example is given to show the effectiveness and applicability of the proposed method.

Key words: random variable, fuzzy reliability, advanced first order second moment (AFOSM), convectional reliability, fuzzy variable