Performance Evaluation of HWMA Control Chart based on AR(p) with Trend Model to Detect Shift Process Mean

Abstract

The main goal of this study is to establish explicit solutions for the average run length (ARL) of the Homogenously Weighted Moving Average control chart when subjected to autoregressive with trend process. The accuracy of the explicit formula for the ARL is evaluated in comparison to the numerical integral equation method. To evaluate the two approaches, the accuracy percentage was employed. A determination is carried out of the HWMA control chart’s effectiveness using the median run length (MRL), the standard deviation of run length (SDRL), and the average run length (ARL). A comprehensive comparison is performed between the HWMA control chart, the Extended Exponentially Weighted Moving Average (EEWMA), and the cumulative sum (CUSUM) control charts with mean process shifts to illustrate the design and implementation of the HWMA control chart. As criteria for various values of design parameters, the performance of these control charts can also be evaluated using the relative mean index (RMI), the average extra quadratic loss (AEQL), and the performance comparison index (PCI). To evaluate the effectiveness of our explicit formula approach, we employ this formula on copper price data.