Monitoring Packaging Defects in a Logistic Company for the Determination of Type-II Errors

In the logistics sector, defects in packaging can seriously impact product quality, increasing the chances of damage during transit and potentially putting consumers at risk. As a result, poor packaging quality can lead to more product returns, recalls, and waste, which may result in decreasing customer loyalty and the company's reputation. This study introduces an extended <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$c$</tex> control chart with picture fuzzy sets (PFSs) for monitoring packaging quality in the logistics sector. This proposed approach monitors packaging processes in logistics while accounting for uncertainty, demonstrating how fuzzy logic can handle and model this uncertainty effectively. By representing process uncertainty with PFSs, a more sensitive and accurate control chart is achieved. Based on that, the study aims to help packaging operators in the logistics sector identify problems early and intervene with corrective actions as needed, using the proposed extended methodology. The effectiveness of the proposed approach is demonstrated with an illustrative example. Also, to show the performance of it, average run lengths for both in-control and out-of-control scenarios are calculated. Based on the results, the proposed approach increases in overall efficiency and product reliability by reducing type-II errors and allowing better representation of the problem environment under uncertainty.