Theory of Probability and Mathematical Statistics
Properties of highly reliable double system in the event of the work phase distribution of one of alternating processes is exponential
O. O. Kushnir, V. P. Kushnir
Download PDF
Abstract: Some upper bounds for characteristics of reliability of highly reliable double system assuming that the work phase distribution of one of alternating processes is exponential.
Keywords: Renewal process, alternating process, duplicate system, Renyi theorem, semi-Markov process.
Bibliography: 1. N. V. Kartashov, Inequalities in the Renyi theorem, Teor. Veroyatnost. Mat. Stat. 45 (1991), 27–33; English transl. in Theory Probab. Math. Statist. 45 (1991), 23–28.
2. O. O. Kushnir, Estimation of the time to failure distribution function convergence rate in a highly reliable system GI/G/1/0, Teor. Imorvirn. Mat. Stat., 52 (1995), 99–101. (Ukrainian)
3. O. O. Kushnir, V. P. Kushnir Properties of highly reliable systems with protection in the case of Poisson renewal process, Theory Probab. Math. Statist., 96 (2018), 127–132.
4. V. S. Korolyuk and V. V. Korolyuk Stochastic Models of Systems, Springer-Science+Business Media B.V., Mathematics and Its Applications, 1999.
5. O. O. Kushnir, The first failure of a highly reliable system of two elevators, Teor. Imorvirn. Mat. Stat., 59 (1998), 110–116; English transl. in Theory Probab. Math. Statist. 59 (1999), 113–120.
6. I. N. Kovalenko, A. Birolini, Uniform exponential bounds for the pointwise availability of a repairable system, Exploring stochastic laws: Festschrift in honour of the 70th birthday of academician Vladimir Semenovich Korolyuk (A.V. Skorokhod, Yu.V. Borovskikh ed.), VSP, Zeist, 1995, 233–242.
7. J. Ben Atkinson, The transient M/G/1/0 queue: some bounds and approximations for light traffic with application to reliability , Journal of Applied Mathematics and Stochastic Analysis 8 (1995), no.4, 347–359.