Abstract Failure mode and effects analysis (FMEA) is a prospective risk assessment tool which has been widely used within various industries, particularly the aerospace, automotive and healthcare industries. However, the conventional risk priority number (RPN) method has been criticized much for its deficiencies in risk factor weights, computation of RPN, evaluation of failure modes and so on. Therefore ranking of failure modes based on their related risk factors is necessary seeking to overcome the shortcomings and enhance the assessment capability of the traditional FMEA. In this paper, we treat the risk factors and their weights as fuzzy variables and evaluate them using fuzzy linguistic terms. As a result, a new risk priority model is proposed for evaluating the risk of failure modes based on fuzzy set theory and MULTIMOORA method. An empirical case of preventing infant abduction is provided to illustrate the potential applications and benefits of the proposed fuzzy FMEA. The main findings of this article are related with the proposed technique for failure modes assessment and ranking, and application of this technique for the prevention of infant abduction, which is a devastating problem for a healthcare facility.