A methodology combining the benefits of matrix FMEA and fuzzy logic is presented in this paper. The matrix approach is improved to develop a pictorial representation retaining all relevant qualitative and quantitative information of a several FMEA element relationships, which can be described as many-to-many. For example, one failure mode may result in several effects, and one effect may result from several failure modes. The methodology presented also extends the risk prioritization beyond the conventional Risk Priority Number (RPN) method. Fuzzy logic is used for prioritizing failures for corrective actions in FMEA. In RPN method, the criticality assessment is based on the severity, frequency of occurrence and detectability of failure. However, these parameters are here represented as members of a fuzzy set, combined by matching them against rules in a rule base, evaluated with min-max inferencing, and then defuzzified to assess the riskness of the failure. The fundamental problem with RPN technique is that it attempts to quantify risk without adequately quantifying the factors that contribute to risk. In particular cases, RPNs can be misleading. This deficiency can be eliminated by introducing the new technique to calculate criticality rank based on fuzzy logic. The methodology presented is demonstrated by application to an illustrative example.