Skip to main content
SpringerLink
Log in

On k-out-of-n System Under Full Repair and Arbitrary Distributed Repair Time

  • Conference paper
  • First Online:
Distributed Computer and Communication Networks: Control, Computation, Communications (DCCN 2021)

Part of the book series: Lecture Notes in Computer Science ((LNCCN,volume 13144))

Abstract

A k-out-of-n : F renewable system with exponentially distributed life-times, and arbitrary distributed repair times of its components under a partial repair regime has been investigated in the paper [1]. This paper deals with the same model under the full repair regime after the system failure. For this model we use Markovization method, based on adding of supplementary variables for the service process, describing system behavior in our analysis.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 64.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 84.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    Another approach for investigation of this kind of system is also possible and has been demonstrated in [14].

  2. 2.

    We omit here these cumbersome calculations, and demonstrate them with examples in the Sect. 5.

References

  1. Rykov, V., Ivanova, N.: Reliability and sensitivity analysis of a repairable \(k\)-out-of-\(n: F\) system with general life- and repair times distributions. In: Baraldi, P., Di Maio, F., Zio, E. (eds.) Proceedings of the 30th European Safety and Reliability Conference and the 15th Probabilistic Safety Assessment and Management Conference. Copyright Oc ESREL2020-PSAM15 Organizers. Published by Research Publishing, Singapore (2020). ISBN/DOI 978-981-14-8593-0

    Google Scholar 

  2. Vishnevsky, V., Kozyrev, D., Rykov, V., Nguen, Z.: Reliability modeling of the rotary-wing flight module of a high-altitude telecommunications platform. Inf. Technol. Comput. Syst 4(20), 26–38 (2020). (in Russian)

    Google Scholar 

  3. Rykov, V.V., Sukharev, M.G., Itkin, V.Y.: Investigations of the potential application of k-out-of-n systems in oil and gas industry objects. J. Mar. Sci. Eng. 8, 928 (2020). www.mdpi.com/journal/jmse, https://doi.org/10.3390/jmse8110928

  4. Rykov, V., Kochueva, O., Farkhadov, M.: Preventive maintenance of a k-out-of-n system with applications in subsea pipeline monitoring. J. Mar. Sci. Eng. 9, 85 (2021). https://doi.org/10.3390/jmse9010085

    Article  Google Scholar 

  5. Trivedi, K.S.: Probability and Statistics with Reliability. Wiley, New York (2002)

    Google Scholar 

  6. Chakravarthy, S.R., Krishnamoorthy, A., Ushakumari, P.V.: A \(k\)-out-of-\(n\) reliability system with an unreliable server and Phase type repairs and services: the \((N, T)\) policy. J. Appl. Math. Stoch. Anal. 14(4), 361–380 (2001)

    Article  MathSciNet  Google Scholar 

  7. Moustafa, M.S.: Availability of \(K\)-out-of-\(N: G\) systems with exponential failure and general repairs. Econ. Qual. Control. 16(1), 75–82 (2001)

    MathSciNet  MATH  Google Scholar 

  8. Linton, D.G., Saw, J.G.: Reliability analysis of the \(k\) -out-of- \(n: f\) system. IEEE Trans. Reliab. 23, 97–103 (1974)

    Article  MathSciNet  Google Scholar 

  9. Rykov, V.V.: On reliability of renewable systems. In: Vonta I., Ram M. (eds.) Reliability Engineering, Theory and Applications, pp. 173–196 (2018)

    Google Scholar 

  10. Cox, D.R.: The analysis of non-Markovian stochastic processes by the inclusion of supplementary variables. Math. Proc. Cambridge Phil. Soc. 51(3), 433–441 (1955). https://doi.org/10.1017/S0305004100030437

    Article  MathSciNet  MATH  Google Scholar 

  11. Rykov, V., Kozyrev, D., Filimonov, A., Ivanova, N.: On reliability function of a \(k\)-out-of-\(n\) system with general repair time distribution. Prob. Eng. Inf. Sci. 35, 1–18 (2020). https://doi.org/10.1017/S02699648200002

    Article  MathSciNet  Google Scholar 

  12. Rykov, V., Ivanova, N., Kozyrev, D.: Sensitivity analysis of a \(k\)-out-of-\(n\): F system characteristics to shapes of input distribution. In: Lecture Notes in Computer Science (LNCS), vol. 12563, pp. 485–496. Springer, Heidelberg (2020). https://doi.org/10.1007/978-3-030-66471-837

  13. Rykov, V., Filimonov, A.: Hyperbolic systems with multiple characteristics and some of their applications. Manag. Large Syst. 85, 72–86 (2021)

    Google Scholar 

  14. Rykov, V.V.: Decomposable semi-regenerative processes: review of theory and applications to queueing and reliability systems. RT&A 16(2(62)), 157–190 (2021)

    Google Scholar 

  15. Petrovsky, I.G.: Lectures on Theory of Ordinary Differential Equations. Nauka, Moscow (1984).(In Russian)

    Google Scholar 

  16. Rojdenstvensky, B.L., Tanenko, N.N.: Systems of Kvasi-Linear Equations, p. 688. Nauka, Moscow (1978). (In Russian)

    Google Scholar 

  17. Rykov, V., Ivanova, N., Kozyrev, D.: Application of decomposable semi-regenerative processes to the study of \(k\)-out-of-\(n\) systems. Mathematics 9, 1933 (2021). https://doi.org/10.3390/math91611933

    Article  Google Scholar 

Download references

Acknowledgements

The publication has been prepared with the support of the “RUDN University Strategic Academic Leadership Program” and funded by RFBR according to the research projects No.20-01-00575A (recipient V.V. Rykov).

Author information

Authors and Affiliations

  1. Department of Mathematics, Kettering University, Flint, MI, USA

    Boyan Dimitrov

  2. Peoples’ Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya St, Moscow, 117198, Russian Federation

    Vladimir Rykov

  3. Gubkin Oil and Gas Russian State University (Gubkin University), 65 Leninsky prospect, Moscow, 119991, Russian Federation

    Vladimir Rykov

  4. Institute for Transmission Information Problems (named after A.A. Kharkevich) RAS, Bolshoy Karetny, 19, 4, Moscow, Russian Federation

    Vladimir Rykov

Authors
  1. Boyan Dimitrov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Vladimir Rykov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Vladimir Rykov .

Editor information

Editors and Affiliations

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

    Vladimir M. Vishnevskiy

  2. Applied Probability and Informatics Department, RUDN University, Moscow, Russia

    Konstantin E. Samouylov

  3. V.A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences, Moscow, Russia

    Dmitry V. Kozyrev

Rights and permissions

Reprints and permissions

Copyright information

© 2021 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Dimitrov, B., Rykov, V. (2021). On k-out-of-n System Under Full Repair and Arbitrary Distributed Repair Time. In: Vishnevskiy, V.M., Samouylov, K.E., Kozyrev, D.V. (eds) Distributed Computer and Communication Networks: Control, Computation, Communications. DCCN 2021. Lecture Notes in Computer Science(), vol 13144. Springer, Cham. https://doi.org/10.1007/978-3-030-92507-9_26

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-92507-9_26

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-92506-2

  • Online ISBN: 978-3-030-92507-9

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation