S.F. Boev1, R.S. Shafir2, A.A. Markov3, K.I. Veretennikov4, A.R. Buyashkin5

1 JSFC “Sistema” (Moscow, Russia)
2–4 Lomonosov Moscow State University (Moscow, Russia)
5 Moscow State Technological University “STANKIN” (Moscow, Russia)
1 ris@tstu.tver.ru, 2 romanshafir@mail.ru, 3 amarkov2502@gmail.ru, 4 veretennikov.ki22@physics.msu.ru, 5arsuna@inbox.ru

This paper examines complex information and control systems with a multi-level hierarchical structure. A key feature of these systems is the potential for so-called "cascading failures," where failures of lower-level elements lead to the inability of all functionally related higher-level elements to perform their functions. Both classic works on reliability theory and modern scientific research lack a universal algorithm for calculating the reliability indicators of such systems.

Goal – the objective of this study is to develop a universal algorithm for calculating the probability of failure-free operation and the availability factor of hierarchical information and control systems with an arbitrary number of levels.

Probabilistic methods for assessing the reliability of complex systems are applied in this work. To account for cascading failures of system elements, the law of total probability is utilized. An analytical expression has been derived to calculate the probability of failure-free operation and the availability factor for systems with any number of hierarchical levels, considering cascading element failures. For the software implementation of the developed algorithm, the paper provides recommendations for calculating the reliability indicators of large-scale systems, allowing for the avoidance of numerical data type overflow issues.

The developed algorithm can be used for reliability calculations during the design of multi-level hierarchical information and control systems, as well as for analyzing the reliability of various technical configurations to select the most dependable option. In the case of repairable systems, the algorithm allows for the justification of quantitative requirements for spare parts, tools, and accessories (SPTA) to meet specified availability factor requirements.

Boev S.F., Shafir R.S., Markov A.A., Veretennikov K.I., Buyashkin A.R. Algorithm for calculating the probability of failure-free operation and the availability factor of an information and control system with a hierarchical structure and cascading failures. Nonlinear World. 2026. V. 24. № 2. P. 22–30. DOI: https:// doi.org/10.18127/ j20700970-202602-03 (In Russian)

1. Viktorova V.S., Stepanyanc A.S. Modeli i metody rascheta nadezhnosti tekhnicheskih sistem M.: LENAND. 2016. 256 c. (In Russian)
2. Polovko A.M., Gurov S.V. Osnovy teorii nadezhnosti: Ucheb. posobie dlya studentov vuzov, obuchayushchihsya po napravleniyu podgot. 230100 (654600) «Informatika i vychisl. tekhnika». Izd. 2-e, pererab. i dop.. M.: BHV-Peterburg. 2006. 702 s. EDN QMERHX (In Russian).
3. Gnedenko B.V., Belyaev Yu.K., Solov'ev A.D. Matematicheskie metody v teorii nadezhnosti: osnovnye harakteristiki nadezhnosti i ih statisticheskij analiz. Izd. 2-e, ispr. i dop. M.: LIBROKOM. 2012. 582 s. (Fiziko-matematicheskoe nasledie: matematika (teoriya veroyatnostej)) (In Russian).
4. Ushakov I.A. Veroyatnostnye modeli nadezhnosti informacionno-vychislitel'nyh sistem. M.: Radio i Svyaz'. 1991. 132 c. (In Russian)
5. Telyshev D.V. Prognozirovanie i ocenka nadezhnosti apparatov mekhanicheskogo zameshcheniya funkcii serdca. Izv. vuzov. Ser.: Elektronika. 2020. T. 25. № 1. S. 58–68. DOI 10.24151/1561-5405-2020-25-1-58-68 (In Russian).
6. Gel'fman T.E., Pirhavka A.P., Skripachev V.O. Analiz effektivnosti metodov obespecheniya nadezhnosti retranslyatora sputnika svyazi. Russ. Technol. J. 2023. V. 11(1). P. 51−59. https://doi.org/10.32362/2500-316X-2023-11-1-51-59 (In Russian)
7. Gel'fman T.E., Pirhavka A.P. Ocenka effektivnosti skol'zyashchego rezervirovaniya radioelektronnyh sredstv. Russ. Technol. J. 2023. V. 11(5). P. 45−53. https://doi.org/10.32362/2500-316X-2023-11-5-45-53 (In Russian)
8. Telyshev D.V. Prognozirovanie i ocenka nadezhnosti apparatov mekhanicheskogo zameshcheniya funkcii serdca. Izv. vuzov. Ser.: Elektronika. 2020. T. 25. № 1. S. 58–68. DOI 10.24151/1561-5405-2020-25-1-58-68 (In Russian).
9. Dorozhko I.V., Kopejka A.L., Zaharova E.A. Imitacionnaya model' dlya ocenivaniya pokazatelej nadezhnosti slozhnyh tekhnicheskih kompleksov s uchetom pokazatelej kontrolya i diagnostirovaniya. Izv. Tul'skogo gos. un-ta. Ser.: Tekhnicheskie nauki. 2018. № 10. S. 490–498. EDN VOXXZW (In Russian).
10. Dorozhko I.V. Kopejka A.L. Issledovanie koefficienta gotovnosti slozhnyh tekhnicheskih kompleksov s pomoshch'yu imitacionnoj modeli, razrabotannoj v srede Stateflow paketa MatLab. Intellektual'nye tekhnologii na transporte. 2018. № 3(15). S. 18–26. EDN YRMQOT (In Russian).
11. Yakimov V.L., Mal'cev G.N. Gibridnye setevye struktury i ih ispol'zovanie pri diagnostirovanii slozhnyh tekhnicheskih sistem. Informatika i avtomatizaciya. 2022. № 21(1). S. 126–160 (In Russian).
12. GOST 27.507-2015. Nadezhnost' v tekhnike (SSNT) Zapasnye chasti, instrumenty i prinadlezhnosti. Ocenka i raschet zapasov (In Russian).