Abstract
A heterogeneous double redundant hot standby renewable system with Marshall-Olkin failure model is considered. In one of previous papers the stationary characteristics for such system for the case of exponential lifetime distributions has been found and its asymptotic insensitivity to the shape of its components repair time distributions has been studied. In this paper the problem of asymptotic insensitivity of such system for both life- and repair time general distributions with the help of simulation method is studied.
V. Rykov—The publication has been prepared with the support of the “RUDN University Program 5-100” and funded by RFBR according to the research projects No. 17-01-00633, No. 17-07-00142, and No. 18-07-00576.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
Sevast’yanov, B.A.: An ergodic theorem for markov processes and its application to telephone systems with refusals. Theory Probab. Appl. 2(1), 104–112 (1957)
Kovalenko, I.N.: Investigations on Analysis of Complex Systems Reliability, p. 210. Naukova Dumka, Kiev (1976). (in Russian)
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). https://doi.org/10.1007/978-3-642-35980-4_17
Koenig, D., Rykov, V., Schtoyn, D.: Queueing Theory, p. 115. Gubkin University Press, Moskva (1979). (in Russian)
Gnedenko, B.V.: On cold double redundant system. Izv. AN SSSR. Texn. Cybern. 4, 3–12 (1964). (in Russian)
Gnedenko, B.V.: On cold double redundant system with restoration. Izv. AN SSSR. Texn. Cybern. 5, 111–118 (1964). (in Russian)
Solov’ev, A.D.: On reservation with quick restoration. Izv. AN SSSR. Texn. Cybern. 1, 56–71 (1970). (in Russian)
Kalashnikov, V.V.: Geometric Sums: Bounds for Rare Events with Applications: Risk Analysis, Reliability, Queueing, p. 256. Kluwer Academic Publishers, Dordrecht (1997)
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
Rykov, V.V., Kozyrev, D.V.: Analysis of renewable reliability systems by markovization method. In: Rykov, V.V., Singpurwalla, N.D., Zubkov, A.M. (eds.) ACMPT 2017. LNCS, vol. 10684, pp. 210–220. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-71504-9_19
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.) ECMS 2017 Proceedings of European Council for Modeling and Simulation, pp. 701–705 (2017). https://doi.org/10.7148/2017-0701
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. Inform. Phys. 3, 65–77 (2014). (in Russian)
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). https://doi.org/10.1007/978-3-319-13671-4_13
Marshall, A., Olkin, I.: A multivariate exponential distribution. J. Am. Stat. Assoc. 62, 30–44 (1967)
Rykov, V., Kozyrev, D.: On sensitivity of steady-state probabilities of a cold redundant system to the shapes of life and repair time distributions of its elements. In: Pilz, J., Rasch, D., Melas, V., Moder, K. (eds.) IWS 2015. PROMS, vol. 231, pp. 391–402. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-76035-3_28
Efrosinin, D., Rykov, V., Vishnevskiy, V.: Sensitivity of reliability models to the shape of life and repair time distributions. In: 9th International Conference on Availability, Reliability and Security (ARES 2014), pp. 430–437. IEEE (2014). https://doi.org/10.1109/ARES.2014.65. Published in CD: 978-I-4799-4223-7/14
Barlow, R., Proschan, F.: Statistical Theory of Reliability and Life Testing. Silver Spring, Redwood City (1981)
Singpurwalla, N.: Reliability and Risk: A Bayesian Perspective. Wiley, Chichester (2006)
Lai, C.D., Balakrishnan, N.: Continuous Bivariate Distributions, 2nd edn. Springer, New York (2009). https://doi.org/10.1007/b101765
Gupta, A., Zeung, W., Hu, Y.: Probability and Statistical Models: Foundations for Problems in Reliability and Financial Mathematics. Birkhauser, Basel (2010)
McNeil, A., Frey, L., Embrechts, P.: Quantitative Risk Management, 2nd edn. Princeton University Press, Princeton (2015)
Li, X., Pellerey, F.: Generalized Marshall-Olkin distributions and related bivariate aging properties. J. Multivar. Anal. 102, 1399–1409 (2011)
Lin, J., Li, X.: Multivariate generalized Marshall-Olkin distributions and copulas. Methodol. Comput. Appl. Probab. 16, 53–78 (2014)
Kolev, N., Pinto, J.: A weak version of bivariate lack of memory property. Braz. J. Probab. Stat. (2017, accepted)
Rykov, V.: On steady state probabilities of double redundant renewable system with Marshal-Olkin failure model. In: Accepted for publication in Proceedings of IWS-2018 (2018)
Kozyrev, D., Rykov, V., Kolev, N.: Reliability function of renewable system with Marshal-Olkin failure model. Reliab.: Theory Appl. 13(1(48)), 39–46 (2018)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer Nature Switzerland AG
About this paper
Cite this paper
Rykov, V., Zaripova, E., Ivanova, N., Shorgin, S. (2018). On Sensitivity Analysis of Steady State Probabilities of Double Redundant Renewable System with Marshall-Olkin Failure Model. In: Vishnevskiy, V., Kozyrev, D. (eds) Distributed Computer and Communication Networks. DCCN 2018. Communications in Computer and Information Science, vol 919. Springer, Cham. https://doi.org/10.1007/978-3-319-99447-5_20
Download citation
DOI: https://doi.org/10.1007/978-3-319-99447-5_20
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-99446-8
Online ISBN: 978-3-319-99447-5
eBook Packages: Computer ScienceComputer Science (R0)