Analysis of Renewable Reliability Systems by Markovization Method

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10684)


Markovization method is used for heterogeneous double redundant hot standby renewable reliability system analysis. The time dependent, stationary and quasi-stationary probability distributions for the system are calculated.


Markovization method Reliability system Time-dependent Stationary and quasi-stationary probabilities 



The publication was prepared with the support of the “RUDN University Program 5–100”, and was financially supported by the Russian Foundation for Basic Research according to the research projects Nos. 17-07-00142 and 17-01-00633.


  1. 1.
    Sevast’yanov, B.A.: An ergodic theorem for markov processes and its application to telephone systems with refusals. Theor. Prob. Appl. 2(1), 104–112 (1957)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Kovalenko, I.N.: Investigations on analysis of complex systems reliability. Kiev: Naukova Dumka, p. 210 (1976). (in Russian)Google Scholar
  3. 3.
    Rykov, V.: Multidimensional alternative processes reliability models. In: Dudin, A., Klimenok, V., Tsarenkov, G., Dudin, S. (eds.) BWWQT 2013. CCIS, vol. 356, pp. 147–156. Springer, Heidelberg (2013). CrossRefGoogle Scholar
  4. 4.
    Koenig, D., Rykov, V., Schtoyn, D.: Queueing Theory. M.: Gubkin University Press, p. 115 (1979). (in Russian)Google Scholar
  5. 5.
    Gnedenko, B.V.: On cold double redundant system. Izv. AN SSSR. Texn. Cybern. 4, 312 (1964). (in Russian)Google Scholar
  6. 6.
    Gnedenko, B.V.: On cold double redundant system with restoration. Izv. AN SSSR. Texn. Cybern. 5, 111–118 (1964). (in Russian)Google Scholar
  7. 7.
    Solov’ev, A.D.: On reservation with quick restoration. Izv. AN SSSR. Texn. Cybern. 1, 56–71 (1970). (in Russian)Google Scholar
  8. 8.
    Rykov, V., Ngia, T.A.: On sensitivity of systems reliability characteristics to the shape of their elements life and repair time distributions. Vestnik PFUR. Ser. Math. Inf. Physics. 3, 65–77 (2014). (in Russian)Google Scholar
  9. 9.
    Efrosinin, D., Rykov, V.: Sensitivity analysis of reliability characteristics to the shape of the life and repair time distributions. In: Dudin, A., Nazarov, A., Yakupov, R., Gortsev, A. (eds.) ITMM 2014. CCIS, vol. 487, pp. 101–112. Springer, Cham (2014). Google Scholar
  10. 10.
    Efrosinin, D., Rykov, V., Vishnevskiy, V.: Sensitivity of reliability models to the shape of life and repair time distributions. In: 9-th International Conference on Availability, Reliability and Security (ARES 2014), pp. 430–437. IEEE (2014). Published in CD: 978-I-4799-4223-7/14. 2014.65
  11. 11.
    Rykov, V., Kozyrev, D., Zaripova, E.: Modeling and simulation of reliability function of a homogeneous hot double redundant repairable system. In: Paprika, Z.Z., Horák, P., Váradi, K., Zwierczyk, P.T., Vidovics-Dancs, Á., Rádics, J.P. (eds.) Proceedings of the European Council for Modeling and Simulation, ECMS 2017 (2017).
  12. 12.
    Rykov, V., Kozyrev, D.: On Markovizastion method application to reliability function calculation. Markov Processes and Related Fields. Presented for publicationsGoogle Scholar
  13. 13.
    Felle, W.: An Introduction to Probability Theory and Its Applications, vol. 1, 3rd edn. Wiley, Hoboken (1968)Google Scholar
  14. 14.
    Kozyrev, D.V.: Analysis of asymptotic behavior of reliability properties of redundant systems under the fast recovery. Math. Inf. Sci. Phys. 3, 49–57 (2011). (in Russian). Bulletin of Peoples’ Friendship University of Russia SeriesGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Department of Applied Probability and InformaticsPeoples’ Friendship University of Russia (RUDN University)MoscowRussia
  2. 2.Gubkin Russian State University of Oil and GasMoscowRussia
  3. 3.V.A. Trapeznikov Institute of Control Sciences of Russian Academy of SciencesMoscowRussia

Personalised recommendations