This paper presents a novel, efficient fuzzy rule-based Bayesian reasoning (FuRBaR) approach for prioritizing failures in failure mode and effects analysis (FMEA). The technique is specifically intended to deal with some of the drawbacks concerning the use of conventional fuzzy logic (i.e. rule-based) methods in FMEA. In the proposed approach, subjective belief degrees are assigned to the consequent part of the rules to model the incompleteness encountered in establishing the knowledge base. A Bayesian reasoning mechanism is then used to aggregate all relevant rules for assessing and prioritizing potential failure modes. A series of case studies of collision risk between a floating, production, storage, and off loading (FPSO) system and a shuttle tanker caused by technical failure during tandem off loading operation is used to illustrate the application of the proposed model. The reliability of the new approach is tested by using a benchmarking technique (with a well-established fuzzy rule-based evidential reasoning method), and a sensitivity analysis of failure priority values.