Enhanced performance of mixed HWMA-CUSUM charts using auxiliary information

Quality control (QC) is a systematic approach to ensuring that products and services meet customer requirements. It is an essential part of manufacturing and industry, as it helps to improve product quality, customer satisfaction, and profitability. Quality practitioners generally apply control charts to monitor the industrial process, among many other statistical process control tools, and to detect changes. New developments in control charting schemes for high-quality monitoring are the need of the hour. In this paper, we have enhanced the performance of the mixed homogeneously weighted moving average (HWMA)-cumulative sum (CUSUM) control chart by using the auxiliary information-based (AIB) regression estimator and named it MHCAIB. The proposed MHCAIB chart provided an unbiased and more efficient estimator of the process location. The various measures of the run length are used to judge the performance of the proposed MHCAIB and to compare it with existing AIB charts like CUSUMAIB, EWMAAIB, MECAIB (mixed AIB EWMA-CUSUM), and HWMAAIB. The Run length (RL) based performance comparisons indicate that the MHCAIB chart performs relatively better in monitoring small to moderate shifts over its competitor's charts. It is shown that the chart's performance improves with the increase in correlation between the study variable and the auxiliary variable. An illustrative application of the proposed MHCAIB chart is also provided to show its implementation in practical situations.