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The main objective of this paper is to propose a new risk priority model for prioritizing failures in failure mode and effects analysis (FMEA) on the basis of fuzzy evidential reasoning (FER) and belief rule-based (BRB) methodology. The technique is particularly intended to resolve some of the shortcomings in fuzzy FMEA (i.e., fuzzy rule-based) approaches. In the proposed approach, risk factors like occurrence (O), severity (S), and detection (D), along with their relative importance weights, are described using fuzzy belief structures. The FER approach is used to capture and aggregate the diversified, uncertain assessment information given by the FMEA team members; the BRB methodology is used to model the uncertainty, and nonlinear relationships between risk factors and corresponding risk level; and the inference of the rule-based system is implemented using the weighted average-maximum composition algorithm. The Dempster rule of combination is then used to aggregate all relevant rules for assessing and prioritizing the failure modes that have been identified in FMEA. A case study concerning an ocean going fishing vessel in a marine industry is provided and conducted using the proposed model to illustrate its potential applications and benefits.