Automation and Remote Control

, Volume 79, Issue 7, pp 1270–1286 | Cite as

Reliability Models and Analysis of Systems with Protection

  • V. S. ViktorovaEmail author
  • N. V. Lubkov
  • A. S. Stepanyants
Control in Technical Systems


We consider models of reliability for systems with protection; these models feature various factors for increasing accident-free operation and efficiency. We determine limit values for the accident-free index that can be provided only by increasing the reliability of the protection system and the protected technological object. We show that high requirements for accident-free operation can be guaranteed if there is a control of the operability of the protection system and its recovery after a failure is detected. Experiments based on the method of Markov processes with rewards confirm our theoretical conclusions and allow us to determine the range of rational values of maintenance parameters.


reliability multilevel models Markov processes with rewards protection systems 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Pravila yadernoi bezopasnosti reaktornykh ustanovok atomnykh stantsii (Nuclear Safety Rules for Nuclear Power Plant Reactors), PNAEG-1-024-90 (PBYa RU AS-89), Moscow: Gospromatomnadzor, 1991.Google Scholar
  2. 2.
    Viktorova, V.S., Sverdlik, Yu.M., and Stepanyants, A.S., Analyzing Reliability for Systems with Complex Structure on Multilevel Models, Autom. Remote Control, 2010, vol. 71, no. 7, pp. 1410–1414.MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Viktorova, V.S. and Stepanyants, A.S., Multilevel Modeling of System Reliability, Datch. Sist., 2014, no. 6 (181), pp. 33–37.Google Scholar
  4. 4.
    Viktorova, V.S., Lubkov, N.V., and Stepanyants, A.S., Program for Analyzing the Reliability and Efficiency on Multilevel Markov Models, Software State Registration Certificate no. 2016663241, Russia, reg. 29.11.2016.Google Scholar
  5. 5.
    Lubkov, N.V., Spiridonov, I.B., and Stepanyants, A.S., Influence of Control Characteristics on Reliability Parameters of Systems, Proc. MAI, 2016. no. 85. php?ID=67501
  6. 6.
    Volik, B.G., Buyanov, B.B., Lubkov, N.V., et al., Metody analiza i sinteza struktur upravlyayushchikh sistem (Methods of Analysis and Synthesis of Control Systems Structure), Moscow: Energoatomizdat, 1988.Google Scholar
  7. 7.
    Howard, R.A., Dynamic Programming and Markov Processes, New York: Technology Press and Wiley, 1960. Translated under the title Dinamicheskoe programmirovanie i markovskie protsessy, Moscow: Sovetskoe Radio, 1964.Google Scholar
  8. 8.
    Buyanov, B.B., Zlobinskii, V.I., Lubkov, N.V., and Stepanyants, A.S., ASU TP. Otsenka nadezhnosti i effektivnosti na osnove modelei markovskikh protsessov s dokhodami (MPD-metod) (Industrial Control System. Estimating Reliability and Efficiency Based on Markov Process Models with Rewards), RM 25431–87, Moscow: Minpribor, 1987.Google Scholar
  9. 9.
    Reibman, A., Smith, R., and Trivedi, K., Markov and Markov Reward Model Transient Analysis: An Overview of Numerical Approaches, Eur. J. Oper. Res., 1989, vol. 40, no. 2, pp. 257–267.MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Nicol, D., Sanders, W., and Trivedi, K., Model-Based Evaluation from Dependability to Security, IEEE Transact. Dependable Secure Comput., 2004, vol. 1, no. 1, pp. 48–65.CrossRefGoogle Scholar
  11. 11.
    Sato, N. and Trivedi, K., Accurate and Efficient Stochastic Reliability Analysis of Composite Services Using Compact Markov Reward Model Representations, IEEE Int. Conf. Servic. Comput. (SCC 2007), 2007, pp. 114–121.CrossRefGoogle Scholar
  12. 12.
    Rykov, V. and Efrosinin, D., On Optimal Control of Systems on Their Life Time, in Recent Advances in System Reliability, Springer Series in Reliability Engineering, Lisnianski, A. and Frenkel, I., Eds., London: Springer, 2012, pp. 307–319.CrossRefGoogle Scholar
  13. 13.
    Toledano, S., Gartsman, I., Avitan, G., et al., On Markov Reward Approach to Failure Criticality Importance Assessment for Aging Multi-state System, Second Int. Sympos. Stochast. Models Reliabilit. Engineer., Life Scie. Oper. Management (SMRLO), 2016, pp. 375–379.Google Scholar
  14. 14.
    Viktorova, V.S., Lubkov, N.V., and Stepanyants, A.S., Reliability of Technical Systems. Providing and Analyzing, Proc. 16th Intl. Conf CAD/CAM/PDM-2016, Moscow: Inst. Probl. Upravlen., OOO Analytik, 2016, pp. 14–18.Google Scholar
  15. 15.
    Viktorova, V.S., Lubkov, N.V., and Stepanyants, A.S., Software for the Analysis of Reliability, Efficiency, and Safety Based on Models of Markov Processes with Rewards, Software State Registration Certificate no. 2016663244, Russia; reg. 29.11.2016.Google Scholar

Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  • V. S. Viktorova
    • 1
    Email author
  • N. V. Lubkov
    • 1
  • A. S. Stepanyants
    • 1
  1. 1.Trapeznikov Institute of Control SciencesRussian Academy of SciencesMoscowRussia

Personalised recommendations