Reducing the Stochastic Coal Output Model Using the Convolution of Probability Density Functions

The construction of stochastic models and the use of stochastic simulations for their analysis constitute research methods used in the analysis of stochastic processes. These methods can be applied to processes carried out in underground mines. For mining processes, carried out, e.g., in hard coal mines, it is noticed that the influence of factors generally referred to as geological–mining and technical–organizational may cause a given process to be treated as not fully defined (not necessarily in terms of the process technology, but, e.g., taking into account the time taken for its implementation). This article draws attention to the possibilities of reducing the stochastic model based on the use of the properties of the convolution of probability density functions. Functions that were considered appropriate for describing the processes discussed based on time-based studies were presented. The mechanism of operation of the proposed model reduction was discussed. Reduction carried out in this way eliminates the need to analyze these parts of the model, e.g., using the stochastic simulation method. This reduction leads to simplification of the model and the calculations, which translates into the effectiveness of the research.