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Failure mode and effects analysis (FMEA) is a prospective risk assessment tool used to identify, assess, and eliminate potential failure modes (FMs) in various industries to improve security and reliability. However, the traditional FMEA method has been criticized for several shortcomings and even the improved FMEA methods based on predefined linguistic terms cannot meet the needs of FMEA team members' diversified opinion expressions. To solve these problems, a novel FMEA method is proposed by integrating Bayesian fuzzy assessment number (BFAN) and extended gray relational analysis-technique for order preference by similarity to ideal solution (GRA-TOPSIS) method.First, the BFANs are used to flexibly describe the risk evaluation results of the identified failure modes. Second, the Hausdorff distance between BFANs is calculated by using the probability density function (PDF). Finally, on the basis of the distance, the extended GRA-TOPSIS method is applied to prioritize failure modes. A simulation study is presented to verify the effectiveness of the proposed approach in dealing with vague concepts and show its advantages over existing FMEA methods. Furthermore, a real case concerning the risk evaluation of aero-engine turbine and compressor blades is provided to illustrate the practical application of the proposed method and particularly show the potential of using the BFANs in capturing FMEA team members' diverse opinions. KEYWORDSBayesian fuzzy assessment number, failure mode and effects analysis, GRA-TOPSIS, Hausdorff distance, probability density function

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