A Probabilistic Approach to Overestimation by an Imperfect Inspector Subject to Random Defective Rates

• Published in: Symmetry (Basel) Vol. 17; no. 2; p. 284
• Main Author: Koo, Kyo-Chan
• Format: Journal Article
• Language: English
• Published: Basel MDPI AG 01.02.2025
• Subjects: Accuracy; Additive manufacturing; Defects; Error analysis; Expected values; Inspection; Inventory control; Logistics; Mathematical models; Order quantity; Parameter sensitivity; Probability theory; Quality control; Random variables; Sensitivity analysis; Statistical analysis; Steel production; Supply chains
• ISSN: 2073-8994; 2073-8994
• DOI: 10.3390/sym17020284

This study investigates overestimations in defect inspections performed by imperfect inspectors, particularly in scenarios involving random defective rates. Mathematical models are developed under two key assumptions: (1) inspection errors are either constant or uniformly distributed and (2) defective rates follow a random uniform distribution. Four analytical models are used to evaluate the probability of overestimation (PO) and identify critical defect rate thresholds (CFBs). The findings reveal that the PO approaches 100% as defect rates approach zero, irrespective of inspection error characteristics. Sensitivity analysis demonstrates model robustness under varying error distributions and parameter changes. Addressing practical concerns, this research highlights the need to revise inspection schemes to mitigate biases, especially in industries with stringent quality control standards, such as electronics and pharmaceuticals. Recommendations include integrating probabilistic error models and adopting dynamic calibration systems to improve inspection accuracy. By providing a theoretical foundation for tackling overestimation, this study has significant implications for improving fairness and efficiency in global supply chains.