This article is cited in 2 scientific papers (total in 2 papers)
On stability of highly reliable systems
M. I. Freidlin
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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Theory of Probability and its Applications, 1976, 20:3, 572–583
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
\paper On stability of highly reliable systems
\jour Teor. Veroyatnost. i Primenen.
\jour Theory Probab. Appl.
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L. V. Zhivoglyadova, M. I. Freidlin, “Kraevye zadachi s malym
parametrom dlya diffuzionnogo protsessa s otrazheniem”, UMN, 31:5(191) (1976), 241–242
M. I. Freidlin, “The averaging principle and theorems on large deviations”, Russian Math. Surveys, 33:5 (1978), 117–176
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