Impact of Early Inspection on the Performance of Production Systems – Insights from an EPQ model

Zsuzsanna Hauck, Boualem Rabta, Gerald Reiner

Publication: Scientific journalJournal articlepeer-review


Most manufacturing systems contain a critical operation in their production where defects are more likely to occur. Letting the defective items pass through further stages of the process can result in a significant loss of time, materials, and money. Therefore, this study considers a manufacturing process with an early stage of quality control.

Unlike most academic literature, the presented model considers the impact of the screening time on both screening costs and defect detection rate via different linear and nonlinear functions to derive a better understanding of those dependencies. We develop and analyze a mathematical model to determine the optimal lot size jointly with the optimal screening time during production. We run multiple numerical examples to illustrate the impact of various parameters of the model. Sensitivity analysis shows the robustness of the proposed model with respect to small changes in its parameters.

Managerial insights are dealing with highly relevant trade-offs. Firstly, devoting more time to the initial screening increases the inspection cost but allows a greater proportion of defects to be detected. Secondly, discarding defective items at an early production stage decreases production costs at subsequent stages. In addition, the maximum gain is obtained when the relationships between the screening time and the cost, as well as the efficiency of the detection method, are well-understood. Our results also highlight the importance of careful estimation of the defect rate. A higher proportion of defective items increases the required screening time, lot size, and total cost.
Original languageEnglish
Pages (from-to)670 - 687
JournalApplied Mathematical Modelling
Publication statusPublished - 2022

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