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Keywords = serial Bernoulli production line

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25 pages, 8928 KiB  
Article
Accuracy of Semi-Analytical and Numerical Approaches in the Evaluation of Serial Bernoulli Production Lines
by Viktor Ložar, Neven Hadžić, Tihomir Opetuk and Vedran Slapničar
Mathematics 2021, 9(13), 1461; https://doi.org/10.3390/math9131461 - 22 Jun 2021
Cited by 6 | Viewed by 1809
Abstract
The manufacturing industry has a great impact on the economic growth of countries. It is, therefore, crucial to master the skills of the production system by mathematical tools that enable the evaluation of the production systems’ performance measures. Four mathematical approaches toward the [...] Read more.
The manufacturing industry has a great impact on the economic growth of countries. It is, therefore, crucial to master the skills of the production system by mathematical tools that enable the evaluation of the production systems’ performance measures. Four mathematical approaches toward the modeling of steady-state behavior of serial Bernoulli production lines were considered in this study, namely, the analytical approach, the finite state method, the aggregation procedure, and numerical modeling. The accuracy of the performance measures determined using the semi-analytical methods and the numerical approach was validated using numerous theoretical examples and the results obtained using the analytical model. All of the considered methods demonstrated relevant reliability, regardless of the different theoretical backgrounds. Full article
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23 pages, 4514 KiB  
Article
A Finite State Method in the Performance Evaluation of the Bernoulli Serial Production Lines
by Neven Hadžić, Viktor Ložar and Filip Abdulaj
Appl. Sci. 2020, 10(18), 6602; https://doi.org/10.3390/app10186602 - 21 Sep 2020
Cited by 7 | Viewed by 3047
Abstract
Research on the performance measure evaluation of Bernoulli serial production lines is presented in this paper. Important aspects of the modeling and analysis using transition systems within the Markovian framework are addressed, including analytical and approximation methods. The “dimensionality curse” problems of the [...] Read more.
Research on the performance measure evaluation of Bernoulli serial production lines is presented in this paper. Important aspects of the modeling and analysis using transition systems within the Markovian framework are addressed, including analytical and approximation methods. The “dimensionality curse” problems of the large scale and dense transition systems in the production system engineering field are pointed out as one of the main research and development obstacles. In that respect, a new analytically-based finite state method is presented based on the proportionality property of the stationary probability distribution across the systems’ state space. Simple and differentiable expressions for the performance measures including the production rate, the work-in-process, and the probabilities of machine blockage and starvation are formulated. A finite state method’s accuracy and applicability are successfully validated by comparing the obtained results against the rigorous analytical solution. Full article
(This article belongs to the Section Mechanical Engineering)
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