Analytical Explicit Formulas of Average Run Length of DEWMA Control Chart based on Seasonal Moving Average Process

The primary objective of this research is to propose explicit formulas for the Average Run Length (ARL) of the Double Exponentially Weighted Moving Average control chart (DEWMA) for the Seasonal Moving Average process (SMA (Q)L) with exponential white noise. The Numerical Integral Equation by the midpoint rule is employed to compare the results derived from the formulas and evaluate their accuracy using the percentage of accuracy (%Acc). The DEWMA control chart's efficacy is measured by calculating the average run length (ARL), median run length (MRL), and standard deviation of run length (SDRL). Significant agreement was observed between the numerical approximations and the explicit formulations for SMA(2)4 and SMA(3)12 processes. This finding indicates the formulations are sufficiently precise. A comparison of Exponentially Weighted Moving Average (EWMA) and DEWMA control charts relating to mean process variations is performed. For practical data, WTI oil prices are used to determine the efficacy of the explicit formula approach.