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
References
1. Rykov V. Decomposable semi-regenerative processes and their applications. LAMBERT Academic Publishing; 2010.
2. Glynn P.W. A GSMP formalism for discrete event systems. Proceedings of the IEEE 1989;1(77):14-23. DOI: 10.1109/5.21067.
3. Glynn P.W., Haas P.J. Laws of large numbers and functional central limit theorems for generalized semi-Markov processes. Stochastic Models 2006;22(2):201-231. DOI: 10.1080/15326340600648997.
4. Glynn P.W., Haas P.J. On transience and recurrence in irreducible finite-state stochastic systems. ACM Transactions on Modeling and Computer Simulation 2015;4(25):1-19. DOI: 10.1145/2699721.
5. Rykov V. On reliability of a double redundant renewable system. In: Gribaudo M., Sopin E., Kochetkova I., editors. Analytical and Stochastic Modelling Techniques and Applications. ASMTA 2019. Lecture Notes in Computer Science 2020, Vol. 12023. DOI: 10.1007/978-3-030-62885-7_3.
6. Rykov V., Efrosinin D., Stepanova N. et al. On Reliability of a Double Redundant Renewable System with a Generally Distributed Life and Repair Times. Mathematics 2020;8(2). DOI: 10.3390/math8020278.
7. Rykov V., Ivanova N. [On the dependability of a restorable redundant system with general distributions of fault-free operation and restoration times of its elements]. In: [Proceedings of the XXII International A.F. Terpugov Conference]. Tomsk: Tomsk State University; 2023. Pp. 335-340. (in Russ.)
8. David H.A., Nagaraja H.N. Order statistics. 3rd ed. John Wiley & Sons: New York (USA); 2003. DOI: 10.1002/0471722162.
9. Rykov V., Kozyrev D., Filimonov A. et al. On reliability of a k-out-of-n system with general repair time distribution. Probability in the Engineering and Informational Sciences 2020;35(4):885-902. DOI: 10.1017/S0269964820000285.
10. Morozov E., Steyaert B. Stability analysis of regenerative queueing models. Springer, Cham; 2021. DOI: 10.1007/978-3-030-82438-9.
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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