Statistical validity and derivation of balance equations for the two-level model of a production line

Authors

DOI:

https://doi.org/10.15587/1729-4061.2016.81308

Keywords:

PDE model, production line, kinetic equation, production process, multi-moment equations, two-level description, object of labor, technological resources, phase space, assembly-line model

Abstract

A method of constructing a system of multi-moment balance equations, based on the statistical description of a production system is proposed. The need for research is determined by current trends in the development of production systems. The system of equations, which simulates the behavior of the production line for the transient conditions is obtained. It is shown that the resulting balance equations are not closed. The methods of closure of the self-linking chain of balance equations: the small-parameter method and the method of setting the equations of states for higher-order moments are considered. The known models using various methods of closure of the system of equations are analyzed. The model of the production line for the assembly-line production method is considered. The limitations and constraint equations, which enable the transition to single-moment PDE model of description of the assembly line and two-moment PDE model of the production line using the Burgers' equation are shown. The model of the production line for the company with the flow production method is considered. One-, two- and three-moment systems of equations for the two-level model of the production line are obtained. A general system of balance equations for the flow parameters of the production line is constructed.

Author Biography

Oleg Pihnastyi, National Technical University "Kharkiv Polytechnic Institute" Bagalіya str., 21, Kharkiv, Ukraine, 61002

Doctor of Technical Sciences, Associate Professor

Department of Computer Monitoring and logistics

References

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Published

2016-10-30

How to Cite

Pihnastyi, O. (2016). Statistical validity and derivation of balance equations for the two-level model of a production line. Eastern-European Journal of Enterprise Technologies, 5(4 (83), 17–22. https://doi.org/10.15587/1729-4061.2016.81308

Issue

Vol. 5 No. 4 (83) (2016): Mathematics and Cybernetics - applied aspects

Section

Mathematics and Cybernetics - applied aspects

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Copyright (c) 2016 Oleg Piрnastyi

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