On the dependability function of a k≤n|GI|l> system. Part I. Analytical results
https://doi.org/10.21683/1729-2646-2024-24-3-34-43
Abstract
The paper aims to study the primary dependability characteristics of restorable k-out-of-n systems with arbitrary distributions of failure-free time and time to component repair, as well as the total number of repair units. A k-out-of-n system is a system consisting of n components that fails when k out of its (k≤n) components fail. l repair devices are available for restoring failed components. Such a system is denoted as <GIk≤n|GI|l>. The research employed marked Markov processes and the theory of order statistics. Using the proposed approach, a mathematical system model was constructed, marks transformations were mapped and analytic expressions for calculating their distributions were given. In the following part of the paper, using the proposed method, a simulation algorithm will be defined for the purpose of assessing the key dependability characteristics. It will not only enable a numerical study of such systems, but will also help analyse the sensitivity of the dependability characteristics to the initial system parameters.
About the Authors
V. V. Rykov
National University of Oil and Gas (Gubkin University)
Russian Federation
Russian Federation
Vladimir V. Rykov, Doctor of Physics and Mathematics, Professor
65, korp. 1 Leninsky prospekt, Moscow
N. M. Ivanova
V.A. Trapeznikov Institute of Control Sciences of the Russian Academy of Sciences
Russian Federation
Russian Federation
Nika M. Ivanova, Candidate of Physics and Mathematics, Senior Researcher
65 Profsoyuznaya st., Moscow
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Review
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Rykov V.V.,
Ivanova N.M.
On the dependability function of a
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ISSN 1729-2646 (Print)
ISSN 2500-3909 (Online)
ISSN 2500-3909 (Online)
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