Enhancing Average Run Length Efficiency of the Exponentially Weighted Moving Average Control Chart under the SAR(1)L Model with Quadratic Trend

Abstract

This study proposes an explicit formula for finding the Average Run Length (ARL) of Exponentially Weighted Moving Average (EWMA) control charts when applied to seasonal autoregressive processes with a quadratic trend. The ARL values derived from the proposed explicit formula were evaluated for accuracy by comparing them with results from the numerical integral equation (NIE) approach utilizing the Midpoint rule. These methods were assessed using real-world applications in the medical field, along with comprehensive simulations. The results demonstrate that the proposed explicit formula and the NIE method closely align in terms of accuracy, with the explicit formula significantly enhancing computational efficiency compared to the NIE method. These findings suggest that the explicit formula is an effective tool for enhancing control chart performance across multiple disciplines.