Failure Mode and Effects Analysis (FMEA) is a technique used in the manufacturing industry to improve production quality and productivity. It is a method that evaluates possible failures in the system, design, process or service. It aims to continuously improve and decrease these kinds of failure modes. Adaptive Resonance Theory (ART) is one of the learning algorithms without consultants, which are developed for clustering problems in artificial neural networks. In the FMEA method, every failure mode in the system is analyzed according to severity, occurrence and detection. Then, risk priority number (RPN) is acquired by multiplication of these three factors and the necessary failures are improved with respect to the determined threshold value. In addition, there exist many shortcomings of the traditional FMEA method, which affect its efficiency and thus limit its realization. To respond to these difficulties, this study introduces the method named Fuzzy Adaptive Resonance Theory (Fuzzy ART), one of the ART networks, to evaluate RPN in FMEA.