Evaluation of Bernoulli Production Lines with Product Quality Inspection and Rework Stations: Analytical Solution and the Finite State Method

Mathematical modelling of production systems is a central task of production system engineering, especially when considering the competitiveness and effectiveness of production companies aiming at quality management and customer-oriented production.Two different approaches to the modelling of a Bernoulli production line with product quality inspection and rework stations are presented in this study.In the first case, analytical modelling is introduced based on Markov chains and the formulation of constitutive transition matrices.In the second case, an approximative approach is presented by employing the finite state method and formulating new finite state elements.The validation of the approximative approach is performed based on theoretical production lines, and the main findings are employed in a shipyard's plate prefabrication line.The issues of computing requirements and quality-quantity coupling are also discussed, indicating the need for further research in the context of improvability analyses and the design of production systems.