Failure modes and effects analysis (FMEA) has been used to identify the critical risk events and predict a system failure to avoid or reduce the potential failure modes and their effect on operations. The risk priority number (RPN) is the classical method to evaluate the risk of failure in conventional FMEA. RPN, which ranges from 1 to 1000, is a mathematical product of three parameters—severity (S), occurrence (O), and detection (D)—to rank and assess the risk of potential failure modes. However, there are some shortcomings of the conventional RPN method, such as: the RPN elements have many duplicate numbers; violate the assumption of measurement scales; and have not considered the weight of S, O, and D. In order to improve the aforementioned shortcomings of the conventional RPN calculation problem, this paper presents an easy yet effective method to enhance the risk evaluation capability of FMEA. The new method is named exponential risk priority number (ERPN), which uses a simple addition function to the exponential form of S, O, and D to substitute the conventional RPN method, which is a mathematical product of three parameters. Two practical cases are used to demonstrate that the ERPN method can not only resolve some problems of the conventional RPN method but also is able to provide a more accurate and reasonable risk assessment in FMEA.