Enhancing the Performance of an Adjusted MEWMA Control Chart Running on Trend and Quadratic Trend Autoregressive Models.

Control charts are one of the most frequently used tools in statistical process control. They are used to monitor, measure, regulate, improve quality, and identify issues in processes across a variety of industries. The modified exponentially weighted moving average (MEWMA) control chart is frequently used to detect early shifts in the process. Herein, the aim of this study is to adjust a modified exponentially weighted moving average (MEWMA) control chart and derive the explicit formula of the ARL for the autoregressive with trend and quadratic trend models with exponential white noise. The results of the numerical integral equation (NIE) technique and the ARLs produced with the explicit formula were compared. Findings indicated that, in terms of calculation time, the explicit formula using the ARL defeated the NIE technique. The performance of the traditional EWMA, MEWMA, and adjusted MEWMA control charts based on simulation and real-world data was compared using the average run length (ARL) and the standard deviation run length (SDRL). These findings were confirmed by the average extra-quadratic loss (AEQL). Lastly, real-world data on stock prices from Thailand's SET50 and the United States' Nasdag100 index is presented to illustrate how this idea might be used. [ABSTRACT FROM AUTHOR]