Control Charts Using Coupled Exponentially Weighted Moving Averages

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Abstract
The equations governing the construction of control charts for both the mean and the standard deviation or variance of a process using exponentially weighted moving average models are presented. Many different variables for monitoring the control of the standard deviation and variance are discussed. The resulting equations to be solved are nonlinear coupled difference equations. The moments of the stationary solutions which lead to the computation of the control limits are found, and in addition the response to step changes in the mean and variance are discussed. A table containing control chart constants is given. Some of the results obtained are also of importance in the application of exponential smoothing to forecasting.

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