Explicit Analytical Form for the Average Run Length of Double-Modified Exponentially Weighted Moving Average Control Charts Through the MA(q) Process and Applications

The Statistical Process Control (SPC) approach using mathematical modeling proves effective for correlated data, with applications in healthcare, finance, and technology to enhance quality and efficiency. Here, we provide a novel SPC method using mathematical modeling and discuss its use in simulation tests to assess its applicability for tracking processes containing correlated data operating on sophisticated control charts. Particularly, an approach for detecting small shifts in the mean of a process running on the double-modified exponentially weighted moving average (DMEWMA) control chart, which is symmetric about the center line with upper and lower control limits, is of special interest. The computations showed exceptional accuracy, with ARL from the explicit formula closely matching that from the NIE method. Simulation tests assess its applicability in detecting small mean shifts and compare its performance with exponentially weighted moving average (EWMA) and modified exponentially weighted moving average (MEWMA) control charts across various scenarios. For several values of the design parameters, the performances of these three control charts are also compared in terms of the relative average index and relative standard deviation index. The results show that the DMEWMA chart outperforms others for several process mean shifts. The method’s practical use is demonstrated with stock data, highlighting its superior effectiveness in enhancing process monitoring.