Theory of Probability and Mathematical Statistics
On redundant system with renewals
B. V. Dovgaĭ, I. K. Matsak
Download PDF
Abstract: A two units redundant system with repair of general type is considered. Stationary probabilities are found and average for time of sojourn in states is established.
Keywords: redundant system, limit theorems, stationary probabilities
Bibliography: 1. Gnedenko B.V., J.K. Belyaev, A.D. Solovyov, Mathematical Methods in Reliability Theory, M .: "Nauka", 1965. - 524 p.
2.B.Epstein and T.Hosford, textitReliability of some two units reduntant systems, Proc.6-th Nat. Symp. on Reliability and Quality Control, 1960, pp. 466-476.
3.B.V.Gnedenko, About unloaded duplication // Math. USSR Academy of Sciences. Technical cybernetics. - 1964. - № 4. - S. 3-12.
4.B.V.Gnedenko, Аbout duplication with restoration // Math. USSR Academy of Sciences. Those. cybernetics. - 1964. - № 5. - S. 111-118.
5.I.N. Kovalenko, Studies on the reliability analysis of complex systems - Kiev: Science. Dumka, 1975.
6.I.N. Kovalenko, N.Y. Kuznetsov, Modeling highly reliable systems, reliability of technical systems. Directory. - M .: Radio and communication, 1985.
7.V.S. Koroljuk, A.F.Turbin,Semi-Markov processes and their applications, "Naukova Dumka", Kiev -1976.
8.V.S. Koroljuk, A.F.Turbin, Markov renewal processes in systems reliability problems, "Naukova Dumka", Kiev - 1982.
9.V.S. Koroljuk, Stochastic models of systems, "Naukova Dumka", Kiev - 1989.
10.A.D. Solovyev, Reliability of systems with recovery.- In Proc.Key Cybernetics in the service of communism, T.2, M.- L.,"Energy", 1964.
11.A.D. Solovyev, Methods for calculating the reliability of systems, Reliability of Technical Systems. Directory. - M .: Radio and communication, 1985.
12.T.P. Marjanovic, Some questions the reliability of redundant sistem.- Ukr.matem.zhurn. 1963, t.15, number 2, s.145-157.
13.I.K. Matsak, On a single line queuing system with losses, Probability theory and mathematical statistics. - 2014 - Vol. 90. - P. 136-142.
14.D. Cox, V. Smith, Recovery Theory, "Soviet radio" Moscow - 1967/
15.I.I. Gikhman, A.V. Skorokhod, M.I. Yadrenko, Theory of Probability and Mathematical Statistics, Kiev: Vishcha School, 1988.
16.A.N. Kolmogorov, Theory of Probability and Mathematical Statistics,Moscow: "Nauka", 1986.
17.V.V. Anisimov, O.K. Zakusilo, V.S. Donchenko,Elements of queuing theory and asymptotic analysis systems, Kiev: Vishcha School, 1987.
