Homogeneously Mixed Memory Charts with Application in the Substrate Production Process

The cumulative sum (CUSUM) and the exponentially weighted moving average (EWMA) charts are renowned classical memory charts used to monitor small and moderate shifts in the process(s). Mixed memory charts like mixed EWMA-CUSUM (MEC) and mixed CUSUM-EWMA (MCE) are the advanced forms of classical memory charts used to identify shifts quickly in process parameters (location and/or dispersion). Similarly, the homogeneously weighted moving average (HWMA) chart is used for improved process monitoring. It will be worthwhile to combine the HWMA chart features with the existing mixed memory (MCE and MEC) charts to enhance the effectiveness of the mixed memory charts. Therefore, we proposed new charts: mixed HWMA-homogeneously CUSUM (MHWHC) and mixed homogeneously CUSUM-HWMA (MHCHW) charts. The Monte Carlo simulations are used to evaluate the proposed charts' effectiveness. The average run length (ARL) is utilized to compare the proposed MHWHC and MHCHW charts' performance with existing charts such as classical CUSUM and EWMA, MEC, MCE, and HWMA charts. The comparison revealed that the proposed mixed charts are superior to the existing counterparts, specifically monitoring small and moderate shifts. Finally, a real-life application using the manufacturing process's data set is also provided from a practical point of view.