Process equipment and plant maintenance problems are complex in the oil refinery business, since effective maintenance needs to ensure the reliability and availability of the plant. Failure Mode and Effects Analysis (FMEA) is a risk assessment tool that aims to determine possible failure modes, and to reduce the ratio of unknown failure modes, by identifying business-critical systems and the risks of their failures. For the identified failure modes, FMEA determines risk mitigation action(s). The goal is to prevent failure and keep assets and plants running at peak performance by providing fully integrated operations, maintenance, turnarounds, modifications, and asset integrity solutions, during all phases of the asset life cycle. This research was based on FMEA use/application in refineries’ units, and proposes the new fuzzy FMEA risk quantification approach method: “four fuzzy logic system”. The model included a pre-assessment, by sets of fuzzy logic systems, that examined the input parameters that affected the variables of severity, occurrence, and detectability. The proposed model prioritized risks better and addressed the drawbacks of the conventional FMEA method.