Modelling the operation process of fire protection systems using Markov chains

Introduction. In this paper, theoretical and practical aspects of application of Markov chains to modelling of functioning of systems of fire protection of objects on the example of automatic fire extinguishing systems are considered.

Materials and methods. In the process of work, the mathematical apparatus of Markov chains was used and relevant theoretical information was provided. An automatic fire extinguishing system is used as an example and a graph of its states is given, with the help of which it becomes possible to describe theoretically and quantitatively estimate the probabilities of the installation states. The possibility of optimization of such a graph is shown.

Theoretical basis. Determination of probabilities of the conditions of the system under study (in this case, an automatic fire extinguishing system) during operation — readiness mode, temporary shutdown, operation, restoration of readiness and testing, which allows both to assess the effectiveness of its application and to develop the necessary recommendations to improving efficiency.

The results and their discussion. As a result of the study, mathematical expressions and quantitative estimates of the probabilities of the states of an automatic fire extinguishing system were obtained, on the basis of which proposals can be formulated to improve the efficiency of its functioning. Using the optimized Markov chain graph, an analytical expression for estimating the dynamics of the state probability of readiness to use of an automatic fire extinguishing system was obtained.

Conclusions. Using the example of the operation process of an automatic fire extinguishing system, the paper shows the possibility of describing it using a semi-Markov chain in order to assess the probabilities of installation conditions. The possibility of optimizing the chain in order to simplify it and obtain analytical expressions of the dynamics of the probabilities of states is also shown. The presented approach can be used by other researchers to solve similar problems.

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