This study introduces an approach in three phases to cover the disadvantages of the FMEA method including inability to assign different importance to risk factors and incomplete prioritization in uncertain environment. First, the values of Risk Priority Number (RPN) are set through the FMEA method. Then, the Step-wise Weight Assessment Ratio Analysis based on the Z-Number theory (Z-SWARA) method has been done to determine the weights of quintuplet factor. Finally, failures are prioritized using Multi-Objective Optimization by Ratio Analysis based on the Z-number theory (Z-MOORA). The results of implementation of the proposed approach by considering uncertainty and reliability represent a complete prioritization.