Performance Evaluation of Extended EWMA Chart for AR Model with Exogenous Variables

Abstract

The extended exponentially weighted moving average (Extended EWMA) control chart is an effective statistical process control method for monitoring and identifying shifts in process mean, particularly when dealing with autocorrelated data. One key performance measure used to evaluate the capability of control charts in detecting changes is the average run length (ARL). The primary goal of this study is to present the explicit formulas for calculating the ARL of the extended EWMA control chart for autoregressive models with exogenous variables (ARX) and exponential white noise. Another purpose is to compare the performance of the extended EWMA and the classical EWMA control charts under various conditions. The explicit formulas are derived from the ARL integral equation, which is expressed by the Fredholm integral equation. The accuracy of the exact solutions has been verified using the numerical integral equation (NIE) methods that employ four different composite quadrature rules. The result shows that the ARL values obtained from both methods are similar, and the computation time for the proposed explicit formulas is less than 0.001 second. In comparing the two control charts, it is evident that the extended EWMA control chart outperforms the traditional control chart in detecting shifts in the process mean, as confirmed by various overall performance criteria. Additionally, two real datasets, namely SCB stock price and GDP percentage expansions, are applied to demonstrate the effectiveness of the relevant control charts. Doi: 10.28991/HIJ-2024-05-04-03 Full Text: PDF

Keywords

• average run length
• extended ewma chart
• explicit formula
• autoregressive with exogenous variables.