A stochastic model and investigation into the probability distribution of the thickness of boride layers formed on low-carbon steel

The stochastic nature of the thickness of boride layers formed on carbon steel is described in this paper. Additionally, the probability distribution of the layer thickness is studied to determine the best-fit probability distribution. The study combines the use of an empirical model (power-law) and the Markov chain principles, with the purpose of demonstrating that it is feasible to develop a model that represents the non-uniformity of the thickness of boride layers that form on carbon steel. The results indicate that the mean and variance tend to increase when the time or temperature is increased. The findings of this paper demonstrate that an analytical solution to the Kolmogorov's system differential equation can adequately represent the behavior of non-uniform boride layer formed on low-carbon steel, regardless of the temperature or duration of treatment.