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Explicit Formulas of Average Run Length for ARMA(1,1)

S. Phanyaem, Y. Areepong, S. Sukparungsee , G. Mititelu


TExponentially weighted moving average control chart (EWMA) is a popular chart used for detecting shift in the mean of parameter of distributions in quality control. The objective of this paper is to derive explicit formulas of Average Run Length (ARL) for Autoregressive and Moving Average (ARMA) models by using Integral Equation technique. We find explicit formulas of ARL for EWMA control chart and compare the result of the proposed expressions with Numerical Integral Equation. The explicit formulas for ARL that we have derived have been found to be accurate, fast and easy to calculate in comparison with Integral Equation technique.


Exponentially Weighted Moving Average, Autoregressive and Moving Average, Average Run Length, Integral Equation.

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