This paper introduces the Multi-class Neural Additive Models (MNAMs), an extension of Neural Additive Models (NAMs) designed to solve multi-class classification problems while remaining interpretable. The paper firstly presents a set of definitions around model interpretability and associated concepts, concepts on which the proposed machine learning method relies on. The core of the contribution lies in the development of MNAM, a model training method designed to minimize the traditional trade-off between accuracy and interpretability. This method is then put to test in a concrete application: the detection of gearbox degradation levels using vibration data, as part of the PHM Society data challenge of 2023. The obtained results demonstrate that a MNAM reaches higher accuracy performance than other interpretable methods such as Decisional Tree (DT) or Generalized Additive Models (GAMs).