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IWS 2015: Statistics and Simulation pp 391-402

# On Sensitivity of Steady-State Probabilities of a Cold Redundant System to the Shapes of Life and Repair Time Distributions of Its Elements

• Vladimir Rykov
• Dmitry Kozyrev
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 231)

## Abstract

The problem of sensitivity of a redundant system’s reliability characteristics to shapes of their input distributions is considered. In Efrosinin and Rykov, Information Technologies and Mathematical Modelling, 2014, [1] an analytical form for dependence of a two-unit cold standby redundant system reliability characteristics on life and repair time input distributions was obtained and investigated for the case of exponential distribution of one of the time lengths. In the current chapter this study is extended with the help of simulation method to a general case of both non-exponential distributions. Comparison of analytic and simulation results was carried out.

## Keywords

System reliability Steady state probabilities Sensitivity Mathematical modeling and simulation Redundant systems

## Notes

### Acknowledgements

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 No. 17-07-00142 and No. 17-01-00633.

## References

1. 1.
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.) Information Technologies and Mathematical Modelling. (Proceedings of 13th International Scientific Conference ITMM 2014 named after A.F. Terpugov, Anzhero-Sudzhensk, Russia, 20–22 Nov 2014.) Communication in Computer and Information Science, vol. 487, pp. 101–112
2. 2.
Sevast’yanov, B.A.: An ergodic theorem for Markov processes and its application to telephone systems with refusals. Theory Prob. Appl. 2(1), 104 (1957)
3. 3.
Kovalenko, I.N.: Investigations on Analysis of Complex Systems Reliability. Kiev, Naukova Dumka (1976) 210 p. (In Russian)Google Scholar
4. 4.
Rykov, V.: Multidimensional alternative processes as reliability models. In: Dudin, A., Klimenok, V., Tsarenkov, G., Dudin, S. (eds.) Modern Probabilistic Methods for Analysis of Telecommunication Networks. (BWWQT 2013) Proceedings. Series: CCIS 356, p. 147-157. Springer (2013)Google Scholar
5. 5.
Koenig, D., Rykov, V., Schtoyn, D.: Queueing Theory. - M.: Gubkin University Press (1979), 115 p. (In Russian)Google Scholar
6. 6.
Gnedenko, B.V.: On cold double redundant system. Izv. AN SSSR. Texn. Cybern. 4, 312 (1964). (In Russian)Google Scholar
7. 7.
Gnedenko, B.V.: On cold double redundant system with restoration. Izv. AN SSSR. Texn. Cybern. 5, 111118 (1964). (In Russian)Google Scholar
8. 8.
Solov’ev, A.D.: On reservation with quick restoration. Izv. AN SSSR. Texn. Cybern. 1, 5671 (1970). (In Russian)Google Scholar
9. 9.
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. Phys. 3, 65–77 (2014). (In Russian)Google Scholar
10. 10.
Kendall, D.G.: Stochastic processes occurring in the theory of queues and their analysis by the method of embedded Markov chains. Ann. Math. Stat. 24, 338–354 (1953)
11. 11.
Efrosinin, D., Rykov, V., Vishnevskiy, V.: Sensitivity of Reliability Models to the Shape of Life and Repair Time Distributions. (9-th International Conference on Availability, Reliability and Security (ARES 2014), pp. 430–437 (2014) IEEE.
12. 12.
Kozyrev, D.V.: Analysis of Asymptotic Behavior of Reliability Properties of Redundant Systems under the Fast Recovery. Bulletin of Peoples Friendship University of Russia. Series “Mathematics Information Sciences Physics” No.3 (2011), pp.49–57. (In Russian)Google Scholar
13. 13.
Rykov, V.V., Kozyrev, D.V.: Reliability model for hierarchical systems: regenerative approach. Automat. Rem. Control 71(7), 1325–1336 (2010).

## Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

## Authors and Affiliations

1. 1.Peoples’ Friendship University of Russia (RUDN University)MoscowRussian Federation
2. 2.Gubkin Russian State Oil and Gas UniversityMoscowRussia
3. 3.V.A. Trapeznikov Institute of Control Sciences of Russian Academy of SciencesMoscowRussia