Empirical Bayes Prediction for an Attribute Control Chart in Quality Monitoring

A control chart is a valuable statistical tool used in production process control to ensure that products meet quality standards. The c-chart, a specific type of control chart, monitors the number of nonconformities or defects in a production process, thus maintaining product quality. The aim of this study is to introduce an improved c-chart for monitoring nonconformities via the Empirical Bayes approach. An exponential distribution, a special case of the single-parameter gamma distribution, is employed as suitable model for this analysis. To calculate the control limits, the posterior distribution and the predictive density are derived for the unconditional predictive density of the run length. The performance of the c-chart is evaluated via the average run length (ARL) and the standard deviation of the run length (SDRL), with a focus on Phase II analysis, where the chart is used for continuous monitoring of an in-control process. The proposed method’s efficiency is compared with that of existing methods, demonstrating its superiority in achieving large ARL values for an in-control process, particularly when the parameter c is between 5 and 15. The effectiveness of the proposed method increases with increasing inspection unit size, highlighting its robustness and reliability. This enhanced performance highlights the advantages of the Empirical Bayes method in control chart applications, providing a practical and efficient tool for quality monitoring in various industrial processes.