Model of preventive replacements of complex systems elements depending on the operation time and the number of failures

Modern conditions of economic activity of civil aviation operators make actual the problem of economically feasible measures for the organization of technical operation and maintenance of industry equipment, in particular, means of radio technical support for flights and aeronautical telecommunications. At the same time, it is obvious that these means need to be transferred to maintenance on a condition, which, in turn, causes the need to solve the problems related to determining the time for the preventive replacement of elements which diagnosable parameters can reach limit values. This paper presents an algorithm for estimating the optimal replacement of elements using the conditional probabilistic characteristic method for systems with a long period of operation and having a fixed number of failures. An assessment of the accuracy of determining the desired parameter is carried out, provided that its changes have deterministic and random components. The mathematical expectation and variance of the obtained estimate are found. Provided that the time of means operation between restorations (repairs) tends to decrease with an increase in the number of failures, the average number of final failures is obtained that satisfies the Volterra integral equation. To analyze the cost of restoration within the framework of the proposed model, an expression was found for the unit cost of work, depending on the accepted replacement rule and the duration of the expected cycles. Taking into account the mathematical expectation of the latter and associated costs, a two-dimensional optimal replacement rule is formed, and the expediency of using such a replacement period that minimizes the maximum average costs is shown. The obtained results are useful in organizing activities for preventive maintenance of radio technical support for flights and aeronautical telecommunications at various stages of their life cycle.

1. Emelyanov, A.E., Sukhanova, N.V. (2021). Improving the quality of network management of technological processes. Scientific and Technical Journal of Information Technologies, Mechanics and Optics, vol. 21, no. 5, pp. 646–652. DOI: 10.17586/2226-1494-2021-21-5-646-652 (in Russian)

2. Klyachkin, V.N., Karpunina, I.N. (2022). Features of diagnostics of technical systems using multiclass classification. Reliability & Quality of Complex Systems, no. 2 (38), pp. 45–52. DOI: 10.21685/2307-4205-2022-2-5 (in Russian)

3. Shcherbakov, M.V., Sai Van, C. (2020). Architecture of predictive maintenance system of complex multi-object systems in industry 4.0 concept. Software & Systems, no. 2, pp. 186–194. (in Russian)

4. Yurkov, N.K. (2021). The current state of research in the field of creating highly reliable on-board electronic equipment. Reliability & Quality of Complex Systems, no. 4 (36), pp. 5–12. DOI: 10.21685/2307-4205-2021-4-1 (in Russian)

5. Barzilovich, Ye.Yu., Voskoboyev, V.F. (1981). Aircraft systems operation by condition. Moscow: Transport, 197 p. (in Russian)

6. Vorobyev, V.G., Kuznetsov, S.V., Zyl, V.P. (1999). Fundamentals of the theory of technical operation of flight and navigation equipment. Moscow: Transport, 334 p. (in Russian)

7. Emelyanov, V.E., Logvin, A.N. (2014). Technical operation of aviation radio-electronic equipment. Moscow: MORKNIGA, 730 p. (in Russian)

8. Bazilevskiy, M.P. (2020). Multifactor fully connected linear regression models without constraints to the ratios of variables errors variances. Informatics and Applications, vol. 14, no. 2, pp. 92–97. DOI: 10.14357/19922264200213 (in Russian)

9. Maslakov, M.L. (2021). Probabilistic characteristics of non-test adaptive signal correction methods. Journal of Communications Technology and Electronics, vol. 66, no. 2, pp. 145–154. DOI: 10.31857/S0033849421020108

10. Agalarov, Ya.M. (2022). Optimization of the threshold service speed control in the G/M/L queue. Informatics and Applications, vol. 16, no. 1, pp. 73–81. DOI: 10.14357/19922264220111 (in Russian)

11. Bazilevskiy, M.P. (2018). Nonlinear criteria of quasilinear regression models. Modeling, Optimization and Information Technology, vol. 6, no. 4, pp. 185–195. DOI: 10.26102/2310-6018/2018.23.4.015 (in Russian)

12. Venttsel, A.D., Ovcharov, L.A. (1991). The course on the theory of random processes and its engineering applications. Moscow: Nauka, 383 p. (in Russian)

13. Gorbunov, Yu.N. (2019). Improving the accuracy of measurement time intervals of radio reception in the framework of recursive multi-stage Bayesian estimates. RENSIT, vol. 11, no. 3, pp. 291–298. DOI: 10.17725/rensit.2019.11.291 (in Russian)

14. Bosov, A.V. (2022). Linear output control of Markov chain by square criterion. Complete information case. Informatics and Applications, vol. 16, no. 2, pp. 19–26. DOI: 10.14357/19922264220203 (in Russian)

15. Kiselev, V.V. (2022). Method of finding non-dominant solutions in decomposition problems. Mathematical Modeling and Computational Methods, no. 1 (33), pp. 129–140. DOI: 10.18698/2309-3684-2022-1-129140 (in Russian)

16. Barzilovich, Ye.Yu. (1999). Stochastic models for making optimal decisions in economic research. Moscow: MRTSON Gosatomnadzora Rossii, 452 p. (in Russian)

17. Karakeyev, T.T., Kugubayeva, Zh.T. (2020). Regularization of Volterra linear integral equations of the third kind with the multiplication operator to non-decreasing function. Journal of Advanced Research in Technical Science, no. 21, pp. 39–44. DOI: 10.26160/2474-5901-2020-21-33-38 (in Russian)

18. Korypayeva, Yu.V., Aleynikova, N.A., Krasova, N.Ye. (2020). Analysis of mathematical model of reliability of the responsible node of the radio engineering device in the presence of reserve blocks in case of danger of short circuit. Modeling, Optimization and Information Technology, vol. 8, no. 1. DOI: 10.26102/23106018/2020.28.1.009 (accessed: 10.08.2022). (in Russian)

19. Popkov, A.S. (2021). Construction of reachability and controllability sets in a special linear control problem. Vestnik of Saint Petersburg University. Applied Mathematics. Computer Science. Control Processes, vol. 17, no. 3, pp. 294–308. DOI: 10.21638/11701/spbu10. 2021.307 (in Russian)

20. Arguchintsev, A.V., Srochko, V.A. (2022). Procedure for regularization of bilinear optimal control problems based on a nitedimensional model. Vestnik of Saint Petersburg University. Applied Mathematics. Computer Science. Control Processes, vol. 18, no. 1, pp. 179–187. DOI: 10.21638/11701/spbu10.2022.115 (in Russian)

21. Yuan, L.Z. (2007). A discussion on “A bivariate optimal replacement policy for a repairable system”. European Journal of Operational Research, issue 1, pp. 275–276. DOI: 10.1016/j.ejor.2006.03.035

22. Baryshnikov, A.V., Chernyavskiy, A., Borshch, V., Moiseyev, A. (2013). Optimization technique of preventive replacements in the task of planning the repairer's production cycle. Scientific Periodical of the Bauman MSTU Science and Education, no. 8. DOI: 10.7463/0813.0615305 (accessed: 18.11.2022). (in Russian)

23. Sekretarev, Yu.A., Levin, V.M. (2021). Risk-based models of equipment repair management in power supply systems with a mono consumer. Journal of Siberian Federal University. Engineering and Technologies, vol. 14, no. 1, pp. 17–32. DOI: 10.17516/1999494X-0295 (in Russian)

24. Belov, V.F., Gavriushin, S.S., Markova, Y.N., Zankin, A.I. (2022). Modelling of industrial environment with the help of discrete numerical algorithms. Mathematical Modeling and Computational Methods, no. 1 (33), pp. 109–128. DOI: 10.18698/2309-3684-2022-1109128 (in Russian)

25. Stadje, W., Zuckerman, D. (1990). Optimal strategies for some repair replacement models. Advances in Applied Probability, vol. 22, no. 3, pp. 641–656. DOI: 10.2307/1427462