A Novel Two-Sided HWMA Chart Design based on Quadratic Trend AR(p) Model for Mean Monitoring

The main objective of this study is to find an explicit formula for the average run length (ARL) of a Homogenously Weighted Moving Average control chart (HWMA) for an autoregressive process with a quadratic trend under zero state. The two-sided HWMA control chart construction procedure is proposed, and the performance of the control chart is measured using the average run length (ARL), standard deviation run length (SDRL), and mean run length (MRL). In addition, the accuracy of the explicit formula for ARL is compared with the accuracy of the numerical integral equation method. In this research, the performance of the HWMA and modified exponential weighted moving average control charts (MEWMA) for quadratic trend AR(1) and AR(3) models at different levels of process average change is compared. The efficacy of these control charts can additionally be assessed by the EARL, ESDRL, and EMRL metrics. The proposed control chart is applied to simulated and actual data, namely the finished goods inventory index of PCBA.