Geodesic
Asymptotic analysis of reliability of a system with reserve elements and repairing device
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 1 (2021), pp. 16-22 
L. G. Afanas'eva; E. A. Golovastova. Asymptotic analysis of reliability of a system with reserve elements and repairing device. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 1 (2021), pp. 16-22. http://geodesic.mathdoc.fr/item/VMUMM_2021_1_a2/
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     author = {L. G. Afanas'eva and E. A. Golovastova},
     title = {Asymptotic analysis of reliability of a system with reserve elements and repairing device},
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     url = {http://geodesic.mathdoc.fr/item/VMUMM_2021_1_a2/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

The paper deals with a system consisting of $n$ identical elements and one repairing device. While one element is working, other ones stay in reserve. The distribution of working and repairing times of elements are supposed to be exponential. We obtain the asymptotic distribution of the system lifetime under conditions of its high reliability.

[1] Gnedenko B.V., Belyaev Yu.K., Solovev A.D., Matematicheskie metody v teorii nadezhnosti, Nauka, M., 1965

[2] Hutson V.C.L, Pym J.S., Applications of functional analysis and operator theory, Academic Press, London–N.Y.–Toronto, 1980

[3] Dimitrov B., “O chisle otkazov sistemy iz {n} nagruzhennykh elementov”, Izv. Matem. in-ta Bolgar. AN, 12 (1970), 205–210

[4] Sarmah P., Dharmadhikari A.D., “Estimations of parameters of 1-out-of N:G repairable system”, Communs Statist. Theory and Meth., 12:11 (1984), 1365–1374

[5] Vijakumar A., Gopalan M.N., Radhakrishnan R., “Stochastic analysis of {n}-unit repairable system with slow switch”, Stochast. Anal. and Appl., 2:4 (1984), 459–470

[6] Lipsky L., Queueing theory. A linear algebraic approach, Springer, N.Y., 2009

[7] Mehdi J., Stochastic models in queueing theory, Academic Press, Amsterdam–Boston–London, etc., 2003

[8] Hsu Yunq-Lin, Ke Jau-Chuan, Lin Tzu-Hsin, “Redundant systems with general form recovery, delay in restart, failure of switching's and unreliable repair device. Statistical point of view”, Math. and Comput. Simul., 81:11 (2011), 2400–2413

[9] Azarskov V.N., Dzhassim Mukhammed Kasmi, Strelnikov V.P., “Ispolzovanie poryadkovoi statistiki v zadachakh otsenki nadezhnosti rezervirovannykh sistem”, Matem. mashiny i sistemy, 2005, no. 4, 152–156

[10] Boltyanskii V.G., Vilenkin N.Ya., Simmetriya v algebre, MTsNMO, M., 2002