The Stochastic Nature of the Mining Production Process—Modeling of Processes in Deep Hard Coal Mines

The stochastic and undetermined nature of longwall coal mining results from the complex interaction between geological-mining and technical-organizational factors. This interaction causes variability in key parameters of the production process. This article presents three stochastic models developed on the basis of probability density functions, which describe selected process parameters. These mathematical functions serve as the foundation for effective stochastic models, enabling analysis of complex mining operations. The methodology employed in the study involves empirical data collection, statistical analysis, and stochastic simulation, carried out under both laboratory and field conditions. The results include empirical probability functions for output, delays, and crew-dependent productivity, offering insights into process variability and its impact on performance. Each method is characterized by its theoretical foundations, algorithmic structure, and application areas. The models have been validated through statistical tests and operational field data and can be applied as decision-support tools in both scientific research and industrial management. Given the extensive nature of the described methods, the article provides a comprehensive reference list for readers interested in further exploration and practical implementation in mining engineering.