Mixed memory control chart based on auxiliary information for simultaneously monitoring of process parameters: An application in glass field

Cumulative sum (CUSUM) and exponentially weighted moving (EWMA) control charts, known as memory control charts, are famous to monitor a small-to-moderate shift in the process parameters (location and/or dispersion). The EWMA control chart based on auxiliary information denoted as EWMA_AIB⁽¹⁾ and EWMA_AIB⁽²⁾ are advanced forms of the classical EWMA control chart to monitor the process location and dispersion, respectively. Likewise, the combined mixed EWMA-CUSUM (CMEC) control chart is used to simultaneously monitor the process parameters. This study presents the CMEC control chart based on auxiliary information, symbolized as CMEC_AIB control chart for simultaneous monitoring of the process parameters. The proposed CMEC_AIB control chart used EWMA_AIB⁽¹⁾ and EWMA_AIB⁽²⁾ control charts plotting statistics as inputs in the classical CUSUM control charts. The Monte Carlo simulation is used as a computational technique for numerical results. The proposed CMEC_AIB control chart based on average run length performance measure is evaluated against other control charts such as CMEC, combined double mixed EWMA-CUSUM, combined CUSUM, maximum double EWMA, maximum EWMA based on auxiliary information (MaxEWMA_AIB) control and maximum Hybrid EWMA based on auxiliary information (MaxHEWMA_AIB) control charts. The comparison revealed the superiority of the proposed CMEC_AIB control chart. Besides, the CMEC_AIB control chart performs better as the correlation coefficient increases. Likewise, the proposed CMEC_AIB control chart has a better diagnostic ability for possible directions of changes against other control charts. It is vital to mention that some existing control charts such as classical CUSUM, CMEC, and maximum CUSUM are special cases of proposed CMEC_AIB control chart with the specific parameter's values. Finally, to demonstrate the vitality of the proposed study from a practical point of view, a real-life application in the glass bottle manufacturing industry is also provided for users and practitioners.