Geodesic
On stability of highly reliable systems
Teoriâ veroâtnostej i ee primeneniâ, Tome 20 (1975) no. 3, pp. 584-595

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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. 
@article{TVP_1975_20_3_a7,
     author = {M. I. Freidlin},
     title = {On stability of highly reliable systems},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {584--595},
     publisher = {mathdoc},
     volume = {20},
     number = {3},
     year = {1975},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1975_20_3_a7/}
}
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M. I. Freidlin. On stability of highly reliable systems. Teoriâ veroâtnostej i ee primeneniâ, Tome 20 (1975) no. 3, pp. 584-595. http://geodesic.mathdoc.fr/item/TVP_1975_20_3_a7/