Probabilistic Risk Assessment considering statistically random variables is performed for the preliminary design of a Arch Bridge. Component reliabilities of girders have been evaluated using the response surfaces of the design variables at the selected critical sections based on the maximum shear and negative moment locations. Response Surface Method(RSM) is successfully applied for reliability analyses for this relatively small probability of failure of the complex structure, which is hard to be obtained by Monte-Carlo Simulations or by First Order Second Moment Method that can not easily calculate the derivative terms of implicit limit state functions. For the analysis of system reliability, parallel resistance system composed of girders is changed into parallel series connection system. The upper and lower probabilities of failure for the structural system have been evaluated and compared with the suggested prediction method for the combination of failure modes. The suggested prediction method for the combination of failure modes reveals the unexpected combinations of element failures in significantly reduced time and efforts compared with the previous permutation method or system reliability analysis method.