Transient Response of Homogenous and Nonhomogenous Bernoulli Production Lines

The transient response of production systems is of significant importance especially if present advancements in Digital Twinning technology are taken into account. While the steady-state response enables long-term strategic decision making, the transient response enables more detailed simulation con...

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Bibliographic Details
Published in:Mathematics (Basel) 2023-12, Vol.11 (24), p.4945
Main Authors: Hadžić, Neven, Ložar, Viktor, Opetuk, Tihomir, Keser, Robert
Format: Article
Language:English
Subjects:
Analysis
Assembly lines
Assembly-line methods
Bernoulli production line
Business metrics
digital twin
Eigenvalues
finite-state method
key performance indicators
Literature reviews
Manufacturing
Markov analysis
Mathematical models
Preventive maintenance
Production lines
production system engineering
Sensitivity analysis
Transient response
Transients (Dynamics)
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Summary:The transient response of production systems is of significant importance especially if present advancements in Digital Twinning technology are taken into account. While the steady-state response enables long-term strategic decision making, the transient response enables more detailed simulation concerning aspects like production losses and preventive maintenance. This is especially relevant if nonhomogenous aspects of production systems are taken into account. An analytical and approximative solution to the problem of the transient response of homogenous and nonhomogenous Bernoulli production systems is developed in this paper based on the eigendecomposition of transition matrices, the eigenvalue problem, and the finite-state method. In particular, sub-resonant and resonant nonhomogeneous production lines are introduced for the first time. Also, the most significant key performance indicators are developed as functions of the time elapsed from the first cycle. Finally, the relationship between the number of eigenvalues and the accuracy of the results is inspected by employing a sensitivity analysis. The presented theoretical framework was employed in the case of a wood processing facility to present the potential application of the theory in the case of long- and short-term management of production systems.
ISSN:2227-7390
2227-7390
DOI:10.3390/math11244945