Exponentially Weighted Moving Average Chart

The EWMA Control Chart refers to the Exponentially Weighted Moving Average Chart. The common approach is plotting process data as a time series and... 

This pattern, then, is a blend of the weighting functions employed by the Shewhart Control Chart and the CUSUM Chart. We make use of all data points yet more emphasis is placed on the recent ones. Although the Stepwise SPC Chart is a combination of the Shewhart Control Chart and the CUSUM Chart, the Exponentially Weighted Moving Average Chart is a compromise of the two. Figure 6 illustrates the EWMA. 

Crowder, S., A Simple Method for Studying Run Length Distributions of Exponentially Weighted Moving Average Charts, Technometrics, 29, 401-407 (1987). 

The control charts discussed earlier are very useful in the diagnostic aspects of quality process improvement. They can be used to stabilize a process by identifying out-of-control situations. After the process is stabilized and brought in control, further improvement of the process can be achieved by using some special control charts such as the cumulative sum (CUSUM) control chart and the exponentially weighted moving average (EWMA) control chart. These control charts can be used when small shifts in a process are of interest. 

Historically the tools used to learn and create centered primarily around X and R charts and, more recently for the process industries, on Cumsum, sums of the deviation from an actual process average or target value for that process and the exponentially weighted moving average (EWMA). 

In addition to X-charts and R-charts, CUSUM charts are sometimes used. Trends can be detected sooner when using CUSUM charts. More recently, the use o EWMA, exponentially weighted moving averages, is being suggested as being easier to use on the factory floor. 

Two alternatives to the Shewhart control chart, which are more complicated to calculate but generally more effective to detect small shifts, are the Cumulative Sum (or Cusum) control chart and the Exponentially Weighted Moving Average (EWMA) control chart. These control charts will not be discussed here, but are described in standard references. ... 

Exponentially weighted moving average (EWMA) charts, 11,... 

It should be noted that the cumulative sum (CUSUM) and exponential weighted moving average (EWMA) control charts have also been proposed for the use in high-quality processes (Yeh et al. 2008 Szarka and Woodall 2012). However, in some cases, they are very complex and complicated to understand for the practitioners. 

Information about past measurements can also be included in the control chart calculations by exponentially weighting the data. This strategy provides the basis for the exponentially weighted moving-average (EWMA) control chart. Let x denote the sample mean of the measured variable and z denote the EWMA of X. A recursive equation is used to calculate z k),... 

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