Skip to main content
SpringerLink
Log in

Calculation of Reliability Indicators in Nonmonotone Logical-Probabilistic Models of Multilevel Systems

  • CONTROL IN TECHNICAL SYSTEMS
  • Published:
Automation and Remote Control Aims and scope Submit manuscript

Abstract

We consider logical-probabilistic modeling of the reliability behavior of multilevel systems described by nonmonotone functions of the algebra of logic. A method is proposed for calculating the parameter of the flow of transitions to a subset of states specified by a nonmonotone function. An approach to calculating estimates of interval indicators of reliability, efficiency, and safety of multilevel systems on logical-probabilistic models is described. An example of calculating the indicators of the operational availability of a multilevel system with nonmonotone logical criteria for the transition between levels is given. The calculated values of indicators are compared with the results of Markov modeling.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1.
Fig. 2.
Fig. 3.
Fig. 4.

Similar content being viewed by others

REFERENCES

  1. Lisnianski, A., Frenkel, I., and Ding, Y., Multi-State System Reliability Analysis and Optimization for Engineers and Industrial Managers, London: Springer, 2010.

    Book  Google Scholar 

  2. Natvig, B., Multistate Systems Reliability. Theory with Applications, New York: Wiley, 2011.

    Book  Google Scholar 

  3. Viktorova, V.S. and Stepanyants, A.S., Analiz nadezhnosti i effektivnosti mnogourovnevykh tekhnicheskikh sistem (Analysis of Reliability and Efficiency of Multilevel Systems), Moscow: LENAND, 2020.

    Google Scholar 

  4. Volik, B.G., Analysis and provision of technogenic safety of technical objects, Datchiki Sist., 2012, no. 6, pp. 57–63.

  5. Volik, B.G., Buyanov, B.B., Lubkov, N.V., et al., Metody analiza i sinteza struktur upravlyayushchikh sistem (Methods for Analysis and Synthesis of Structures of Control Systems), Moscow: Energoatomizdat, 1988.

    Google Scholar 

  6. Reibman, A.L., Smith, R., and Trivedi, K.S., Markov and Markov reward model transient analysis: an overview of numerical approaches, Eur. J. Oper. Res., 1989, vol. 40, pp. 257–267.

    Article  MathSciNet  Google Scholar 

  7. Viktorova, V.S., Lubkov, N.V., and Stepanyants, A.S., A unified approach to reliability, availability, performability analysis based on Markov processes with rewards, Adv. Syst. Sci. Appl., 2018, vol. 18, no. 4, pp. 13–38. https://ijassa.ipu.ru/index.php/ijassa/article/view/624/467.

    Google Scholar 

  8. Ushakov, I.A., Universal generating function, Izv. Akad. Nauk SSSR. Tekh. Kibern., 1986, no. 3, pp. 37–49.

  9. Ushakov, I.A., The method of generating sequences, Eur. J. Oper. Res., 2000, vol. 125, no. 2, pp. 316–323.

    Article  MathSciNet  Google Scholar 

  10. Levitin, G., The Universal Generating Function in Reliability Analysis and Optimization, London: Springer, 2005.

    Google Scholar 

  11. Lisnianski, A., Lz-transform for a discrete-state continuous-time Markov process and its applications to multi-state system reliability, in Recent Advances in System Reliability. Signatures, Multi-State Systems and Statistical Inference, Lisnianski, A. and Frenkel, I., Eds., London: Springer, 2012, pp. 79–96.

  12. Lisnianski, A., Application of extended universal generating function technique to dynamic reliability analysis of a multi-state system, Second Int. Symp. Stochastic Models Reliab. Eng. Life Sci. Oper. Manage. (SMRLO) (2016), pp. 1–10.

  13. Ryabinin, I.A. and Cherkesov, G.N., Logiko-veroyatnostnye metody issledovaniya nadezhnosti strukturno-slozhnykh sistem (Logical-and-Probabilistic Methods for Studying Reliability of Structurally Complex Systems), Moscow: Radio i svyaz’, 1981.

    Google Scholar 

  14. Mozhaev, A.S. and Gromov, V.N., Teoreticheskie osnovy obshchego logiko-veroyatnostnogo metoda avtomatizirovannogo modelirovaniya sistem (Theoretical Foundations of the General Logical-and-Probabilistic Method of Automated Systems Modeling), St. Petersburg: VITU, 2000.

    Google Scholar 

  15. NUREG-0492. Fault Tree Handbook, 1981.

  16. SAE ARP4761. Guidelines and Methods for Conducting the Safety Assessment Process on Civil Airborne Systems and Equipment. December 1996.

  17. Schneeweiss, W.G., Computing failure frequency, MTBF & MTTR via mixed products of availabilities and unavailabilities, IEEE Trans. Reliab., 1981, vol. 30, pp. 362–363.

    Article  Google Scholar 

  18. Amari, S.V., Generic rules to evaluate system-failure frequency, IEEE Trans. Reliab., 2000, vol. 49, pp. 85–87.

    Article  Google Scholar 

  19. Amari, S.V., Addendum to: Generic rules to evaluate system-failure frequency, IEEE Trans. Reliab., 2002, vol. 51, pp. 378–379.

    Article  Google Scholar 

  20. Rainshke, K. and Ushakov, I.A., Otsenka nadezhnosti sistem s ispol’zovaniem grafov (Assessing the Reliability of Systems Using Graphs), Moscow: Radio Svyaz’, 1988.

    Google Scholar 

  21. Korczak, E., New formula for the failure/repair frequency of multi-state monotone systems and its applications, Control Cybern., 2007, vol. 36, no. 1.

  22. Stepanyants, A.S., Computing the failure flow parameter in logical-and-probabilistic models by the variable recursive growing method, Autom. Remote Control, 2007, vol. 68, no. 9, pp. 1618–1630.

    Article  MathSciNet  Google Scholar 

  23. Viktorova, V.S., Sverdlik, U.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.

    Article  MathSciNet  Google Scholar 

  24. Kumamoto, H. and Henley, E.J., Probabilistic Risk Assessment and Management for Engineers and Scientists, 2nd Ed., New York: Wiley-IEEE Press, 2000.

    Book  Google Scholar 

  25. Wang, D. and Trivedi, K.S., Computing steady-state MTTF for non-coherent repairable systems, IEEE Trans. Reliab., 2005, vol. 54, pp. 506–516.

    Article  Google Scholar 

  26. Stepanyants, A. and Victorova, V., Failure frequency calculation technique in logical-probabilistic models, Reliab & Risk Anal.: Theory & Appl. Electron. J. Int. Group Reliab., 2009, vol. 2, no. 4, pp. 8–23.

    Google Scholar 

  27. Ryabinin, I.A., Nadezhnost’ i bezopasnost’ strukturno-slozhnykh sistem (Reliability and Safety of Structurally Complex Systems), St. Petersburg: Izd S.-Peterb. Univ., 2007.

    Google Scholar 

  28. Gadani, J.P. and Misra, K.B., A heuristic algorithm for system failure frequency, IEEE Trans. Reliab., 1981, vol. 30, pp. 357–361.

    Article  Google Scholar 

  29. Heidtmann, K.D., Smaller sums of disjoint products by subproduct inversion, IEEE Trans. Reliab., 1989, vol. 38, pp. 305–309.

    Article  Google Scholar 

  30. Viktorova, V.S., Lubkov, N.V., and Stepanyants, A.S., Program for calculating technical efficiency indicators on multilevel models of reliability of gas processing equipment, RF State Software Reg. Cert. no. 2017660233, September 19, 2017.

Download references

ACKNOWLEDGMENTS

Dedicated to the memory of Aleksandr Sergeevich Mozhaev.

Author information

Authors and Affiliations

  1. Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, Moscow, 117997, Russia

    V. S. Viktorova & A. S. Stepanyants

Authors
  1. V. S. Viktorova
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. S. Stepanyants
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to V. S. Viktorova or A. S. Stepanyants.

Additional information

Translated by V. Potapchouck

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Viktorova, V.S., Stepanyants, A.S. Calculation of Reliability Indicators in Nonmonotone Logical-Probabilistic Models of Multilevel Systems. Autom Remote Control 82, 827–840 (2021). https://doi.org/10.1134/S0005117921050076

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0005117921050076

Keywords

Search

Navigation