# Semi-Markov analytical model for assessing the quality of the maintenance system and the state of electromechanical complexes

• Volodymyr Kazhan
• Vasyl Stopkin
• Ksenia Kotlyarova
• Alexander Yudin

### Abstract

Analysis of basic research. In practice, the EMC reliability indicators, in particular the failure rate, are time-varying quantities. In view of this, it is necessary to determine such periodicity values and maintenance volumes that would ensure the EMC maximum availability factor. The most adequate mathematical model for analyzing the technical state of EMC can be obtained using the apparatus of the theory of semi-Markov processes (PMF), the basis of which is an oriented graph of the basic states and transitions (GSP) of EMC during operation, which allows to formulate maintenance and maintenance strategies, the content of a separate strategy is determined a specific set of options for all states of EMC.
The purpose of the article. Construction and study of a mathematical model of the EMC operation process to determine the optimal intervals and maintenance and repair strategies.
The main research material. The solution to the first problem includes: building a model for the operation of the EMC; the derivation of the calculated ratio for the availability factor as a function of the technical condition of the EMC and the service station; obtaining an analytical formula for calculating optimal maintenance intervals.
The paper proposes a combination of indicators ranked by importance in the linear programming problem, where the transfer time, which is a function of the SRT parameters and the technical condition of the EMC, is selected as the objective function, and the remaining indicators (readiness level, complex operation costs, and others) are taken into account in the form of restrictions. The result of solving this problem is a set of maintenance and repair options at each step of the operation of the EMC, which comprise the content of the optimal maintenance and repair strategy.Conclusions. An analytical relationship was obtained on the basis of the semi-Markov model of the operation process that allows one to calculate the optimal conditions for ensuring the availability factor of the periodicity of maintenance, which makes it possible to control the unsteady operation of the EMC, to obtain the necessary technical and economic quality indicators to build an adaptive ACS with the technical state of the EMC.

### References

Barlow R., Proshan F. Statistical theory of reliability and reliability tests. Per. from English ON. Ushakov. - M .: Science, 1984. – 27 p.

Kazhan V.E., Kotlyarova I.V. Model for assessing the quality of the maintenance system of electromechanical complexes. Zbіrnik naukovih Prats "Transport", VIP.7. - Dnipropetrovsk, ДДТУЗТ, 2001. - 130 p.

Korolyuk V.S., Turbin A.F. Semi-Markov processes and their applications. Kiev: Naukova Dumka, 1976. – 184 p.

Fadeev D.K., Fadeeva V.N. Computational methods of linear algebra. 2nd ed., M.-L .: Fizmatgiz, 1963. – 734 p.

Published
2020-02-24
Section
Статьи