An enhanced double homogeneously weighted moving average control chart to monitor process location with application in automobile field

The memory control charts, including cumulative sum (CUSUM) and exponentially weighted moving average (EWMA) control charts, are widely used to monitor small-to-moderate shifts in the process location and/or dispersion. The homogenously weighted moving average (HWMA) control chart is the advanced form of the EWMA control chart to monitor process location shifts. Besides, the auxiliary information-based memory control charts efficiently monitor process location shifts. The objective of this study is to propose an auxiliary information based double HWMA, symbolized as (Formula presented.) control chart to further enhance the monitoring of process location shifts. The (Formula presented.) control chart is modeled by mixing the auxiliary information-based HWMA plotting statistic features into the other HWMA control chart. For numerical results, Monte Carlo simulations are used as a computational technique. Famous performance measures including average run length ((Formula presented.)), extra quadratic loss, relative (Formula presented.), and performance comparison index are used to compare the performance of proposed (Formula presented.) control chart against other control charts including classical CUSUM and EWMA, mixed (Formula presented.) - (Formula presented.), auxiliary information based EWMA ((Formula presented.)), HWMA, auxiliary information based HWMA ((Formula presented.)), and double HWMA control charts. The comparisons revealed that the proposed control chart outperformed other control charts, especially for small-to-moderate process location shifts. An automobile braking system application is also provided for users and practitioners to demonstrate the importance of the proposed study from a practical perspective.