Properties of a highly reliable system with duplication and exponential failure-free periods of one of the alternating processes
Authors:
O. O. Kushnir and V. P. Kushnir
Translated by:
S. V. Kvasko
Journal:
Theor. Probability and Math. Statist. 100 (2020), 133-140
MSC (2010):
Primary 60K20; Secondary 90B25
DOI:
https://doi.org/10.1090/tpms/1101
Published electronically:
August 5, 2020
Full-text PDF
Abstract |
References |
Similar Articles |
Additional Information
Abstract: Some upper bounds for characteristics of reliability of a highly reliable system with duplication are obtained for the case where the distribution of the duration of the failure-free period of one of the alternating processes is exponential.
References
- N. V. Kartashov, Inequalities in the Rényi theorem, Teor. Veroyatnost. i Mat. Statist. 45 (1991), 27–33 (Russian); English transl., Theory Probab. Math. Statist. 45 (1992), 23–28. MR 1168444
- O. O. Kushnir, Estimates for the convergence rate of the distribution function of the refusal moment in the high-reliable system $GI/G/I/0$, Teor. Ĭmovīr. Mat. Stat. 52 (1995), 99–101 (Ukrainian, with Ukrainian summary); English transl., Theory Probab. Math. Statist. 52 (1996), 105–107. MR 1445542
- O. O. Kushnīr and V. P. Kushnīr, Study of the properties of a highly reliable system with protection in the case of a Poisson renewal process, Teor. Ĭmovīr. Mat. Stat. 96 (2017), 125–130 (Ukrainian, with English, Russian and Ukrainian summaries); English transl., Theory Probab. Math. Statist. 96 (2018), 127–132. MR 3666876, DOI https://doi.org/10.1090/tpms/1038
- Vladimir S. Korolyuk and Vladimir V. Korolyuk, Stochastic models of systems, Mathematics and its Applications, vol. 469, Kluwer Academic Publishers, Dordrecht, 1999. MR 1753470
- O. O. Kushnīr, The first failure of a highly reliable system of two elevators, Teor. Ĭmovīr. Mat. Stat. 59 (1998), 110–116 (Ukrainian, with Ukrainian summary); English transl., Theory Probab. Math. Statist. 59 (1999), 113–120 (2000). MR 1793770
- Igor N. Kovalenko and Alessandro Birolini, Uniform exponential bounds for the pointwise availability of a repairable system, Exploring stochastic laws, VSP, Utrecht, 1995, pp. 233–242. MR 1714008
- J. Ben Atkinson, The transient $M/G/1/0$ queue: some bounds and approximations for light traffic with application to reliability, J. Appl. Math. Stochastic Anal. 8 (1995), no. 4, 347–359. MR 1363658, DOI https://doi.org/10.1155/S1048953395000311
References
- N. V. Kartashov, Inequalities in the Rényi theorem, Teor. Veroyatnost. Mat. Stat. 45 (1991), 27–33; English transl. in Theory Probab. Math. Statist. 45 (1991), 23–28. MR 1168444
- O. O. Kushnir, Estimates of the rate of convergence of the distribution function of the refusal moment in a highly reliable system GI/G/1/0, Teor. Imovirnost. Matem. Statyst. 52 (1995), 99–101; English transl. in Theory Probab. Math. Statist. 52 (1996), 105–107. MR 1445542
- O. O. Kushnir and V. P. Kushnir, Properties of highly reliable systems with protection in the case of Poisson renewal process, Teor. Imovirnost. Matem. Statyst. 96 (2017), 125–130; English transl. in Theory Probab. Math. Statist. 96 (2018), 127–132. MR 3666876
- V. S. Korolyuk and V. V. Korolyuk, Stochastic Models of Systems, Springer-Science+Business Media B. V., Dordrecht, 1999. MR 1753470
- O. O. Kushnir, The first failure of a highly reliable system of two elevators, Teor. Imovirnost. Mat. Stat. 59 (1998), 110–116; English transl. in Theory Probab. Math. Statist. 59 (1999), 113–120. MR 1793770
- I. N. Kovalenko and 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 and Yu. V. Borovskikh eds.), VSP, Zeist, 1995, 233–242. MR 1714008
- J. Ben Atkinson, The transient M/G/1/0 queue: some bounds and approximations for light traffic with application to reliability, J. Appl. Math. Stoch. Anal. 8 (1995), no. 4, 347–359. MR 1363658
Similar Articles
Retrieve articles in Theory of Probability and Mathematical Statistics
with MSC (2010):
60K20,
90B25
Retrieve articles in all journals
with MSC (2010):
60K20,
90B25
Additional Information
O. O. Kushnir
Affiliation:
Department of Higher Mathematics, Institute of Automatics, Cybernetics and Computer Engineering, National University of Water and Environmental Engineering, Soborna Street, 11, Rivne, 33028 Ukraine
Email:
kuchniroo@gmail.com
V. P. Kushnir
Affiliation:
Department of Higher Mathematics, Institute of Automatics, Cybernetics and Computer Engineering, National University of Water and Environmental Engineering, Soborna Street, 11, Rivne, 33028 Ukraine
Email:
a{_}vp{_}kushnir@meta.ua
Keywords:
Renewal process,
alternating process,
system with duplication,
Rényi’s theorem,
semi-Markov process
Received by editor(s):
January 31, 2019
Published electronically:
August 5, 2020
Article copyright:
© Copyright 2020
American Mathematical Society
