Abstract: In order to analyze the effect of the epistemic uncertainty of the random input variables' distribution parameters on the structure system, the fuzzy variables are introduced to describe the epistemic uncertainty and the membership levels are employed to measure the degree of the epistemic uncertainty. Two effect indicators, main effect and total effect, for the output response and failure probability are proposed at each possibility level, respectively, and then their relationships with the membership levels are investigated in detail. Finally the expected effect indicators are presented to define the effect of each parameter on the system. In order to reduce the computational cost of the proposed indicators, a new method is proposed by the Taylor expansion for the moments of the output response. Three examples are utilized to demonstrate the reasonability of the proposed indices and the efficiency of the proposed method.