The purpose of this paper is to propose a modified version of Failure Mode and Effects Analysis (FMEA) to alleviate its drawbacks. FMEA is an important tool in risk evaluation and finding the priority of potential failure modes for corrective actions. In the proposed method, the Universal Generating Function (UGF) approach has been used to improve the assessment capability of the conventional Risk Priority Number (RPN) in ranking. The new method is named as URPN. It generates the most number of unique values in comparison with the previous methods and considers relative importance for the parameters while it is easy to compute. More unique numbers help to avoid from having the same priority level for different failure modes which represent various risk levels. A case study has been employed to demonstrate that the URPN not only can improve the shortcomings but also is able to provide accurate values for risk assessment. Copyright (c) 2015 John Wiley & Sons, Ltd.