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Teor. Veroyatnost. i Primenen., 1975, Volume 20, Issue 3, Pages 584–595 (Mi tvp3197)  

This article is cited in 2 scientific papers (total in 2 papers)

On stability of highly reliable systems

M. I. Freidlin

Moscow

Abstract: A system consisting of a large number of elements of two kinds is considered. In the course of time elements become defective and are replaced by new ones. The state of the system is a point on the plane with coordinates equal to the numbers of defective elements of each kind. System functions regularly as long as its state belongs to a certain domain on the plain. Refusal intensity, restitution speed and domain depend on a parameter. Under certain assumptions providing high reliability of the system, the principal terms of the logarithmic asymptotics of the system average working time, the probability of its normal functioning during a fixed time interval and some other characteristics are computed.

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English version:
Theory of Probability and its Applications, 1976, 20:3, 572–583

Bibliographic databases:

Received: 28.02.1974

Citation: M. I. Freidlin, “On stability of highly reliable systems”, Teor. Veroyatnost. i Primenen., 20:3 (1975), 584–595; Theory Probab. Appl., 20:3 (1976), 572–583

Citation in format AMSBIB
\Bibitem{Fre75}
\by M.~I.~Freidlin
\paper On stability of highly reliable systems
\jour Teor. Veroyatnost. i Primenen.
\yr 1975
\vol 20
\issue 3
\pages 584--595
\mathnet{http://mi.mathnet.ru/tvp3197}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=383531}
\zmath{https://zbmath.org/?q=an:0353.60086}
\transl
\jour Theory Probab. Appl.
\yr 1976
\vol 20
\issue 3
\pages 572--583
\crossref{https://doi.org/10.1137/1120062}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. L. V. Zhivoglyadova, M. I. Freidlin, “Kraevye zadachi s malym parametrom dlya diffuzionnogo protsessa s otrazheniem”, UMN, 31:5(191) (1976), 241–242  mathnet  mathscinet  zmath
    2. M. I. Freidlin, “The averaging principle and theorems on large deviations”, Russian Math. Surveys, 33:5 (1978), 117–176  mathnet  crossref  mathscinet  zmath
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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