This paper uses the Hidden Markov Model to model an industrial process seen as a discrete event system. Different graphical structures based on Markov automata, called topologies, are proposed. We designed a Synthetic Hidden Markov Model based on a real industrial process. This Synthetic Model is intended to produce industrial maintenance observations (or "symbols"), with a corresponding degradation indicator. These time series events are shown as Markov chains, also called "signatures". The production of symbols is generated by using a Uniform and a Normal distribution. Hence, we implemented these various symbols in proposed topologies using Baum-Welch learning algorithm decoding by Forward Variable and Segmental K-means learning, decoding by Viterbi. Through different measurements on model outputs, these frameworks (a topology with a learning & decoding algorithm and a distribution) are compared to determine the best part of criteria applied to observations. Assessment results show significant differences between the various frameworks studied. After determining the most relevant framework, we developed an industrial application and compared it with the best model framework found. Finally, we propose a model adjustment to fit the industrial maintenance activities studied. Our aim is to produce the best Synthetic Model framework to be used to improve maintenance policy, worker safety and process reliability in the industrial sector.
