CUSUM charts for detecting special causes in integrated process control

Abstract

Abstract This paper investigates control charts for detecting special causes in an ARIMA(0, 1, 1) process that is being adjusted automatically after each observation using a minimum mean‐squared error adjustment policy. It is assumed that the adjustment mechanism is designed to compensate for the inherent variation due to the ARIMA(0, 1, 1) process, but it is desirable to detect and eliminate special causes that occur occasionally and produce additional process variation. It is assumed that these special causes can change the process mean, the process variance, the moving average parameter, or the effect of the adjustment mechanism. Expressions are derived for the process deviation from target for all of these process parameter changes. Numerical results are presented for sustained shifts, transient shifts, and sustained drifts in the process parameters. The objective is to find control charts or combinations of control charts that will be effective for detecting special causes that result in any of these types of parameter changes in any or all of the parameters. CUSUM charts designed for detecting specific parameter changes are considered. It is shown that combinations of CUSUM charts that include a CUSUM chart designed to detect mean shifts and a CUSUM chart of squared deviations from target give good overall performance in detecting a wide range of process changes. Copyright © 2009 John Wiley & Sons, Ltd.

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