Mathematical model of reliability of human-machine system under reduced efficiency of its work is generalized

Authors

  • A. I. Boyko National University of Life and Environmental Sciences of Ukraine image/svg+xml
  • A. V. Novitskiy National University of Life and Environmental Sciences of Ukraine image/svg+xml

Abstract

Abstract. The article presents the analysis of scientific research aimed at ensuring the reliability of "human-machine" systems.
A mathematical model of the reliability of the ergot system "human-machine" was developed for revealing the influence of its parameters on the dynamic characteristics of reliability. Indicators are set when the system gradually loses its initial parameters. The designated graph of states and transitions of the system "human-machine" is constructed in various possible states. The system can be located in two basic states of workable and disabled. To simplify the solution of the tasks of the mathematical description of the behavior of the ergot system, fictitious states are additionally introduced. In the mathematical modeling of the description of work for systems, the following assumptions are adopted. Bounces and restorations are simpler Markovsky, system restoration begins immediately after its failure, the restored system does not give in to its characteristics of the new, inclusion in the work of the system occurs immediately after the completion of the restoration process.
The model is described by stochastic differential equations for the probability balance of Kolmogorov states and transitions. The solution of the system of equations is carried out in the Laplace-Carson transformations. Probabilities of states in the form of transitions from the originals to the images are found in accordance with the Cramer's rule. The main determinant 

of the system of equations includes a combination of characteristics and is a necessary computational element for determining the dynamic characteristics of reliability.
Key words: reliability, system, human-machine, failure, repair.

References

Ушаков ?. А. Курс теории надежности систем. Москва. ДРОФА. 2008. 240 с.

Половко А. М. Основы теории надежности. Санкт-Петербург. БХВ С-Петербург. 2006. 702 с.

Руденко Ю. Н., Ушаков ?. А. Надежность систем энергетики. Москва. Наука. 1989. 253 с.

Рябинин ?. А. Надежность и безопасность структурно-сложных систем. Санкт-Петербург. Политехника. 2000. 247 с.

Черкесов Г. Н. Основы теории надежности автоматизированных систем управления. Ленинград. ЛП?. 1975. 219 с.

Леонтьев Л. П. Надежность технических систем. Рига. Знание. 1969. 267 с.

References

Ushakov, I. A. (2008). Course of the theory of system reliability. Moscow. BUSTARD. 240.

Polovko, A. M. (2006). Fundamentals of the theory of reliability. Saint-Petersburg. Bkhv-Petersburg. 702.

Rudenko, Yu. N., Ushakov, I. A. (1989). Reliability of energy systems. Moscow. Science. 253.

Ryabinin, S. A. (2000). Reliability and safety of structurally complex systems. Saint-Petersburg. Polytechnic. 247.

Cherkesov, G. N. (1975). Fundamentals of reliability theory of automated control systems. Leningrad. LPI. 219.

Leontiev, L. P. (1969). Reliability of technical systems. Riga. Knowledge. 267.

Downloads

Published

2019-01-24

Issue

Vol. 9 No. 3 (2018)

Section

Статті

License

Relationship between right holders and users shall be governed by the terms of the license Creative Commons  Attribution – non-commercial – Distribution On Same Conditions 4.0 international (CC BY-NC-SA 4.0):https://creativecommons.org/licenses/by-nc-sa/4.0/deed.uk

Authors who publish with this journal agree to the following terms:

  • Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
  • Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
  • Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).