Reliability analysis of mine ventilation fans based on Markov process theory

The reliability of mine ventilation fans plays a crucial role in aerological systems and is determined by a combination of various geological, mining-technological, and structural factors, most of which are stochastic in nature. The problem of quantifying the reliability indicators of mine fan installations is addressed using various mathematical methods for modeling random processes. This study considers the possibility of applying Markov process theory to develop a methodology for calculating the operational reliability of centrifugal main mine ventilation fans, using the VShTs-16 as an example. The limitations of applying Markov processes to reliability analysis are demonstrated, particularly due to the condition of stochastic independence of failures. The use of homogeneous Markov processes has its constraints, since the transition intensities between individual system states are not always constant. In such cases, it is impossible to construct a system of differential equations with time-dependent coefficients. When stochastic dependence is present in failure flows of mechanical systems, the application of Markov process theory remains possible, but the most effective tool for reliability analysis in such cases is the Monte Carlo numerical simulation method.