Bayesian control chart using variable sample size with engineering applications

In this study, we suggested an innovative approach by introducing an Adaptive Exponential Weighted Moving Average (AEWMA) control chart utilizing Variable Sample Size (VSS) under Bayesian methodology. The proposed methodology utilized an integer linear function to dynamically adjust sample sizes according to the AEWMA statistic. Another appealing feature of our adaptive framework is the integration of the smoothing constant of an EWMA chart, which enhances monitoring responsiveness. We reveal the superiority of our recommended control chart by extensive simulations to existing Bayesian EWMA and Bayesian AEWMA control charts using Fixed sample size (FSS). The offered Bayesian VAEWMA control chart is more sensitive to detection improvement, a decrease in the false alarm rate, and overall more effective than the existing methods. These findings provide additional justification for the basic notion that process control statistical tools needed to be dynamic, as the manufacturing process itself was dynamic. The results suggest the importance of introducing adaptive SPC methods in dynamic manufacturing environments. A real data application is performed to evaluate the validity and optimal performance of our recommended chart."Please check article if captured correctly."="Dear Editor we have checked and found corrrect."As per standard instruction, city is required for affiliations; however, this information is missing in affiliations [1, 5]. Please check if the provided city is correct and amend if necessary."Dear Editor we have checked and found correct.  thanks youPlease check and confirm that the authors and their respective affiliations have been correctly identified and amend if necessary."Dear Editor we have checked and found correct. thank you".