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.

中文翻译：

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半分析法和数值法在评估系列伯努利生产线时的准确性

制造业对各国经济增长的影响很大。因此，通过能够评估生产系统性能指标的数学工具来掌握生产系统的技能至关重要。本研究考虑了四种对串行伯努利生产线稳态行为建模的数学方法，即分析方法、有限状态方法、聚合程序和数值建模。使用半分析方法和数值方法确定的性能测量的准确性使用大量理论示例和使用分析模型获得的结果进行了验证。无论理论背景如何，所有考虑的方法都证明了相关的可靠性。