Efficient Monitoring of Autoregressive and Moving Average Process using HWMA Control Chart

Quality control is an essential process for manufacturing and industry because it enhances product quality, consumer satisfaction, and overall profitability. Among many other statistical process control tools, quality practitioners typically employ control charts to monitor the industrial process and detect production changes. Control charts are widely used to detect flaws in many applications, such as distributed circuits and systems, electronic devices, and systems and signals. In this study, we derived an explicit formula for Average Run Length (ARL) of the Homogenously Weighted Moving Average control chart (HWMA) under the ARMA (p,q) process. The accuracy was checked using the numerical integral equation (NIE) technique. The finding showed that the explicit formulas and numerical solutions presented an outstanding level of agreement. However, the computational time for the explicit formulas was approximately one second, which was less than that required for the NIE. Moreover, the performance efficiency of the HWMA control chart is compared with the cumulative sum control chart for ARMA (p, q) processes including ARMA (2,1), ARMA (2,3), and ARMA (1,1) processes. The results found that the HWMA control chart performance is found to be preferable to the CUSUM control chart performance. Additionally, the explicit formula of the HWMA control chart was implemented in a practical application of the count of nonconformities in printed circuit boards (PCBs).