Bayesian Control Chart for Number of Defects in Production Quality Control

This study investigates the extension of the c-chart control chart to Bayesian methodology, utilizing the gamma distribution to establish control limits. By comparing the performance of the Bayesian approach with that of two existing methods (the traditional frequentist method and the Bayesian with Jeffreys method), we assess its effectiveness in terms of the average run lengths (ARLs) and false alarm rates (FARs). Simulation results indicate that the proposed Bayesian method consistently outperforms the existing techniques, offering larger ARLs and smaller FARs that closely approximate the expected nominal values. While the Bayesian approach excels in most scenarios, challenges may arise with large values of the λ parameter, necessitating adjustments to the hyperparameters of the gamma prior. Specifically, smaller values of the rate parameter are recommended for optimal performance. Overall, our findings suggest that the Bayesian extension of the c-chart provides a promising alternative for enhanced process monitoring and control.