As a proactive risk management instrument, failure mode and effect analysis (FMEA) has been broadly utilized to recognize, evaluate and eliminate failure modes of products, processes, systems and services. Nevertheless, the conventional FMEA method suffers from many important deficiencies when used in the real world. First, crisp numbers are adopted to describe the risk of failure modes; but, in many practical situations, it is difficult to obtain exact assessment values due to inherent vagueness in the human judgments. Second, the priority ranking of failure modes is determined based on the risk priority number (RPN), which is questionable and strongly sensitive to the variation of risk factor ratings. Therefore, this paper applies linguistic distribution assessments to represent FMEA team members’ risk evaluation information and employs an improved TODIM (an acronym in Portuguese of interactive and multicriteria decision making) method to determine the risk priority of failure modes. Furthermore, both subjective weights and objective weights of risk factors are taken into account while conducting the risk analysis process. Finally, an empirical case concerning the risk evaluation of a grinding wheel system is presented to demonstrate the practicality and effectiveness of the proposed new FMEA model.