Failure mode and effect analysis (FMEA) is a popular safety and reliability analysis tool in examining potential failures of products, process, designs, or services, in a wide range of industries. While FMEA is a popular tool, the limitations of the traditional Risk Priority Number (RPN) model in FMEA have been highlighted in the literature. Even though many alternatives to the traditional RPN model have been proposed, there are not many investigations on the use of clustering techniques in FMEA. The main aim of this paper was to examine the use of a new Euclidean distance-based similarity measure and an incremental-learning clustering model, i.e., fuzzy adaptive resonance theory neural network, for similarity analysis and clustering of failure modes in FMEA; therefore, allowing the failure modes to be analyzed, visualized, and clustered. In this paper, the concept of a risk interval encompassing a group of failure modes is investigated. Besides that, a new approach to analyze risk ordering of different failure groups is introduced. These proposed methods are evaluated using a case study related to the edible bird nest industry in Sarawak, Malaysia. In short, the contributions of this paper are threefold: (1) a new Euclidean distance-based similarity measure, (2) a new risk interval measure for a group of failure modes, and (3) a new analysis of risk ordering of different failure groups.