An enhanced sum of squares generally weighted moving average chart based on auxiliary information for process monitoring

The AIB-SSEWMA chart is an auxiliary information-based (AIB) sum of squares exponentially weighted moving average (SSEWMA) chart using correlated auxiliary information to effectively monitor the shifts in the process mean and/or variability of a normally distributed process. The main focus of this study is proposed to combine an AIB sum of squares generally weighted moving average (AIB-SSGWMA) chart with the properties of the GWMA chart into an AIB-SSEWMA chart. Numerical simulations indicate that the AIB-SSGWMA chart based on average run lengths (ARLs) performs uniformly better than its counterparts, such as the AIB-SSEWMA, SSGWMA, and SSEWMA charts in detecting small process mean and/or variability shifts. In addition, the proposed chart is sensitive to small upward shifts in the mean as well as variability, as compared to the existing AIB-MaxGWMA chart. An example is used to illustrate the efficiency of the proposed AIB-SSGWMA chart in detecting small process shifts.