Имитационное моделирование процесса функционирования технической ячейки с необесценивающими отказами

V. Ya. Kopp; M. V. Zamorenov; N. I. Chalenkov

doi:10.22213/2410-9304-2020-1-57-64

Authors

V. Y. Kopp
M. V. Zamorenov
N. I. Chalenkov

DOI:

https://doi.org/10.22213/2410-9304-2020-1-57-64

Keywords:

simulation model, semi-Markov system, technological cell, state phase space, AnyLogic

Abstract

The paper describes the method of phase enlargement of semi-Markov systems that does not require the determination of the stationary distribution of the embedded Markov chain. Phase enlargement is the equivalent replacement of a semi-Markov system with a common phase state space, a system with a discrete state space that has the same characteristics as the original system. A lemma on the distribution function of the difference of random variables is presented. Based on the lemma, the application of the formula for the difference of a random variable and a difficult recovery process is described. A method of phase enlargement of regenerating and non-regenerating semi-Markov systems is proposed, which does not include the stage of determining the stationary distribution of the embedded Markov chain for systems with a common phase space. Based on the method of phase enlargement of semi-Markov systems proposed by the authors, the operation of a technological cell with non-depreciating failures is considered. A mathematical description of the system and the simulation results by the proposed method and using simulation are given. During simulation, the time between failures and restoration of the technological cell, as well as the processing time of the product are taken into account. In the AnyLogic environment, simulation models are built in two ways: based on the time diagram of the functioning of the technological cell, as well as on the basis of a time diagram with a graph of cell states. The results of simulation are compared with the method developed by the authors for modeling semi-Markov systems that do not require determining the stationary distribution of the embedded Markov chain for systems with a common phase state space. Comparison of simulation results confirmed the correctness of the construction of the semi-Markov model.

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Kopp V. Ja. The numerical method of the phase integration of nonregenerating semi-Markov systems / V.Ja. Kopp, M.V. Zamoryonov, N.I. Chalenkov. // Transaction of Azerbaijan National Academy of Sciences, Series of Physical-Technical and Mathematical Sciences: Informatics and Control Problems, Vol. XXXVIII, No.6, 2018 www.isi.az/journal/2018/6-00.pdf