Geodesic
On reliability of large-scale nets constructed from identical elements
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 5 (2019), pp. 56-62

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We study the reliability of large-scale structures constructed from identical elements. We consider the structures constructed by serial-parallel extensions and fractal extensions. The number of consecutive connections and the number of parallel connections are presented as infinitely large quantities. It is shown that the reliability of ultimately obtained structures depends on the ratio of these quantities. For the practical application of fractal multiplication in the construction of systems of large reliability, the properties of modules with a number of elements of no more than five have been studied. The results of the work are used for fire-security alarm of complex ground and underground multistory buildings.
Keywords: reliability of complex electric circuits, series-parallel systems, reliability of fractals multiplying structures. 
@article{IVM_2019_5_a4,
     author = {V. A. Rodin and S. V. Sinegubov},
     title = {On reliability of large-scale nets constructed from identical elements},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {56--62},
     publisher = {mathdoc},
     number = {5},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2019_5_a4/}
}
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V. A. Rodin; S. V. Sinegubov. On reliability of large-scale nets constructed from identical elements. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 5 (2019), pp. 56-62. http://geodesic.mathdoc.fr/item/IVM_2019_5_a4/