Numerical Integral Equation Methods of Average Run Length on EWMA Control Chart for Seasonal Moving Average Process with Exogenous Variables
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Abstract
The purpose of this research is to evaluate the method for estimating the average run length (ARL) of an exponentially weighted moving average control chart using a numerical Integral equation when the process data is a seasonal moving average model with exogenous variables. Four methods are employed: the midpoint rule, the trapezoidal rule, the Gaussian rule, and Simpson's rule. The average run length values obtained using four different methods are compared. The CPU times required to perform the ARL evaluation are also compared. The result indicates that the ARL values obtained using the midpoint rule, the Gaussian rule, and Simpson's rule are very similar. However, the value obtained using the trapezoidal rule is less dissimilar. Additionally, when CPU time is considered, the midpoint and trapezoidal rules are the quickest, about 1–2 seconds. However, Gauss's and Simpson's rules require more CPU time, approximately 5–8 seconds.
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