Exact Run Length Evaluation on Extended EWMA Control Chart for Seasonal Autoregressive Process

Herein, we derive explicit formulas for the average run length (ARL) on an extended exponentially weighted moving average (EWMA) chart running a seasonal autoregressive process of order p (SAR(p)L) with exponential white noise. The observations are from SAR(p)L process. The accuracy of the explicit formulas-derived ARL the numerical integral equation method. Although their accuracies were hardly different, the explicit formulas method required a much shorter CPU time to perform the calculation. Furthermore, the efficiency of the extended EWMA control chart was also compared with that of the conventional EWMA control chart utilizing the explicit formulas technique for the ARL. The results show that for a small shift size in the process mean, detection on the extended EWMA control chart was much earlier than on the standard EWMA control chart. Moreover, the proposed method was applied to the SAR(p)L process with real-world data running on the extended EWMA control chart to demonstrate its efficacy.