Reliability Analysis of an Aging Unit with a Controllable Repair Facility Activation

  • Dmitry Efrosinin
  • Janos Sztrik
  • Mais Farkhadov
  • Natalia Stepanova
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 231)

Abstract

The chapter utilizes the continuous-time Markov chain for modeling the processes of the gradual aging with maintenance on a finite discrete set of an intermediate failure states. The transitions occur according to the birth-and-death process, and the unit fails completely after visiting the last available state. The unit of a multiple and single use is studied. The switching of the repair facility is performed by a hysteresis control policy with two threshold levels for switching on/off the repair server. We provide the expressions for the stationary and non-stationary performance and reliability characteristics, solution of optimization problems, and sensitivity analysis of the reliability function.

Keywords

Reliability function Aging unit Sensitivity analysis Markov chain Average reward 

Notes

Acknowledgements

This work was funded by the Russian Foundation for Basic Research, Project No. 16-37-60072 mol_a_dk, supported by the Austro-Hungarian Cooperation Grant No. 96öu8, OMAA 2017, Stiftung Aktion Österreich-Ungarn.

References

  1. 1.
    C.-H-Wu and J.-C- Ke: Computational algorithm and parameter optimization for a multi-server system with unreliable servers and impatient customers. Journal of computational and Applied Mathematics, 235 (2010), 547-562MathSciNetCrossRefGoogle Scholar
  2. 2.
    D. Efrosinin: Optimal parameters of the degrading unit with state-dependent repair time. Proceedings of the MMR2013, Stellenbosch (2013)Google Scholar
  3. 3.
    Kopnov, V.A.: Optimal degradation processes control by two-level policies. Reliability Engineering and System Safety 66, 1–11 (1999)CrossRefGoogle Scholar
  4. 4.
    Mallik, R.K.: On the solution of a second order linear homogeneous difference equation with variable coefficients. Journal of Mathematical Analysis and Applications 215, 32–47 (1997)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Murphy, D.N.P., Iskandar, B.P.: A new shock damage model: Part II - Optimal maintenance policies. Reliability of Engineering System Safety 31, 211–231 (1991)CrossRefGoogle Scholar
  6. 6.
    Rykov, V., Efrosinin, D.: Degradation models with random life resources. Communications in Statistics-Theory and Methods 39, 398–407 (2010)MathSciNetCrossRefGoogle Scholar
  7. 7.
    V. Rykov and D. Efrosinin: On optimal control of systems on their life time. Recent Advances in System Reliability (Springer, 2011), 307-319Google Scholar
  8. 8.
    T.M. Welte, J. Vatn and J. Heggset: Markov state model for optimization of maintenance and renewal of hydro power components. Proceedings of the 9th International Conference PMAPS, Stockholm (2006)Google Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Dmitry Efrosinin
    • 1
    • 2
  • Janos Sztrik
    • 3
  • Mais Farkhadov
    • 2
  • Natalia Stepanova
    • 4
  1. 1.Johannes Kepler University LinzLinzAustria
  2. 2.Institute of Control SciencesMoscowRussia
  3. 3.University of DebrecenDebrecenHungary
  4. 4.Altai Economics and Law InstituteBarnaulRussia

Personalised recommendations