After testing randomness of our stochastic symbols generated by the synthetic model generator, we have successfully applied these two tests on three different HMM topologies. The first one, uses Aspin-Welch and the second one, uses Kolmogorov-Smirnov test. Given a set of observations sequences simulated by our synthetic model, we verified that the most relevant model had the “goodness of fit” i.e. how well model fits the set of observations sequences. In a statistical way, topology of model 2 is the best one. This corroborates results that model 2 is the one which comes closest to real industrial process in Vrignat et al. (2010). Thus, we specified our analysis from Roblès et al. (2011) paper. This criterion also shown that BaumWelch learning algorithm with Forward Variable decoding gives best results with normal distribution of stochastic symbols. In our work on industrial breakdown prediction.