On the Performance of the Extended EWMA Control Chart for Monitoring Process Mean Based on Autocorrelated Data

The extended exponentially weighted moving average (EEWMA) control chart is an instrument for detection. It can quickly identify small shifts in the process. The benchmark for the control chart's performance is the average run length (ARL). In this paper, we present the efficiency of the EEWMA control chart to detect tiny shifts when the observations are autocorrelated with exponential residuals through the explicit formulas of the ARL. The accuracy of the solution was verified with the numerical integral equation (NIE) method. After that, the ARL effectiveness of the ARL on the EEWMA control chart was expanded to compare with the traditional EWMA control chart. Finally, using two real datasets that indicate the percentages of internet users using Windows 7 and iOS, the applicability of the offered method is shown. Our findings support the notion that the EEWMA control chart performs better when using autocorrelated data to track tiny changes.