Adaptive Bayesian Control Chart for Monitoring Defects in Poisson Process

This study introduces an enhanced Bayesian c-chart framework by incorporating two novel loss functions: the modified squared error loss function and the K loss function to improve the sensitivity and robustness of process monitoring for attribute data. Unlike traditional control charts that rely on fixed assumptions and static thresholds, the proposed Bayesian approaches dynamically update the control limits by integrating prior information with probabilistic loss structures. The study conducts a comprehensive simulation analysis under various process shift magnitudes and inspection unit sizes and evaluates performance using key indicators, including Average Run Length (ARL), Standard Deviation of Run Length (SDRL), Average Expected Quadratic Loss (AEQL), and the Performance Comparison Index (PCI). The results show that the proposed methods significantly outperform both classical and standard Bayesian c-charts, particularly in detecting small and moderate shifts. Furthermore, applying the proposed control charts to real-world industrial data—specifically defect monitoring in aircraft manufacturing—confirms their practical utility and adaptability. This work contributes a novel perspective to statistical process control (SPC) by integrating flexible Bayesian modeling with customized loss functions and offers a powerful alternative for quality assurance in high-stakes production environments.