Statistical Evaluation of Semi-Analytical, Analytical, and Numerical Models of the Serial Production Lines

Production lines are the backbone of the manufacturing industry. To gain the best profit out of a line it is necessary to design each line using the production system engineering. Therefore, three approaches can be used, the numerical, the analytical, and the semi-analytical approach. The aggregation method, finite state method, and the numerical approach are statistically compared concerning the analytical approach using the STATISTICA software. We analyzed the interaction between the input data and the output data for the finite state method in an illustrative example, using a full factorial design and the Design Expert software

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Accuracy of Semi-Analytical and Numerical Approaches in the Evaluation of Serial Bernoulli Production Lines

Mathematics ◽

10.3390/math9131461 ◽

2021 ◽

Vol 9 (13) ◽

pp. 1461

Author(s):

Viktor Ložar ◽

Neven Hadžić ◽

Tihomir Opetuk ◽

Vedran Slapničar

Keyword(s):

Performance Measures ◽

Analytical Approach ◽

Manufacturing Industry ◽

Production Systems ◽

Numerical Approach ◽

Production Lines ◽

State Behavior ◽

Finite State ◽

State Method ◽

Numerical Approaches

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.

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A Finite State Method in the Performance Evaluation of the Bernoulli Serial Production Lines

Applied Sciences ◽

10.3390/app10186602 ◽

2020 ◽

Vol 10 (18) ◽

pp. 6602

Author(s):

Neven Hadžić ◽

Viktor Ložar ◽

Filip Abdulaj

Keyword(s):

Large Scale ◽

Performance Measure ◽

Production Lines ◽

Stationary Probability Distribution ◽

Transition Systems ◽

Serial Production ◽

Work In Process ◽

Finite State ◽

State Method ◽

Serial Production Lines

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.

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