In railway operations, there are several factors that must be analyzed, such as operation cost, maintenance stops, failures, and others. One of these important topics is the analysis of the hot box and hot wheel due to the failure of these components. It can compromise the entire operation, resulting in serious accidents, such as train derailments. Thus, the use of a method that is able to classify a failure is essential for accident prevention. Therefore, as these failures in hot box and hot wheels are binary classification problems and nonlinear data, this work proposes a new method based on the Multilayer Perceptron combined with Set-Membership. The Multilayer Perceptron is very flexible and can be used generally to learn complex problems with the aforementioned characteristics; meanwhile, the Set-Membership leads to reduced computational complexity, fast convergence, and high accuracy. To validate the performance, we compare twelve models applied in eight datasets, seven of which are benchmarks, and one is composed of hot box and hot wheels problems. The results showed that the methods had a good performance when applied to these problems.