Two EWMA charts are usually required to monitor both process mean and variability. In this paper, we propose a new EWMA chart which effectively combines the usual two EWMA charts into one chart. In particular, the new EWMA chart has the property that it is effective in detecting both increases and decreases in mean and/or variability.
Keywords: Average Run Length, Control Charts, Variables Data.
by Gemai Chen, University of Regina, Regina, Saskatchewan S4S 0A2, Canada and Smiley W. Cheng and Hansheng Xie, University of Manitoba, Winnipeg, Manitoba R3T 2N2, Canada
The exponentially weighted moving average (EWMA) control chart for the mean of a process was introduced by Roberts (1959). Through simulation studies, he concludes that the EWMA chart can provide greater sensitivity to small changes in the process mean than the standard Shewhart X-bar chart, but that the EWMA chart is not as effective as the X-bar chart when the changes in the process mean are relatively large.
Many researchers have contributed to the theory and practical use of the EWMA chart. A sample of the researchers include Sweet (1986), Crowder (1987, 1989), Ng and Case (1989), Lucas and Saccucci (1990), Domangue and Patch (1991), Gan (1991), Crowder and Hamilton (1992), Gan (1995), and Steiner (1999). We note that two EWMA charts are usually required to monitor both process mean and variability; however, the joint performance of two EWMA charts has not been studied carefully for sample sizes greater than one except in Gan (1995), where the author clearly demonstrates the inadequacy of certain combination schemes, and suggests a simple procedure to design a combination using a two-sided EWMA chart for the mean and two one-sided EWMA charts for the variability. In addition, Gan (1997) proposes a two-dimensional chart in which EWMA of log(S²) is plotted against EWMA of using an elliptical in-control region. Reynolds and Stoumbos (2001) consider the use of two EWMA charts for individual observations. It seems that no attempt has been made, however, to design one EWMA chart which can monitor both the mean and the variability at the same time and indicate the source and direction of a change whenever a change is detected. In this paper, we propose a new EWMA chart to meet some of the above requirements.
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