Exponentially weighted moving average

For an IIR filter, the parameter T in Eq. (9) tends to infinity. IIR filters can be represented as a function of previous filter outputs and often can be computed with fewer multiplications and reduced data storage requirements compared to a FIR filter. A popular example of an IIR filter is the exponentially weighted moving average (EWMA) or exponential smoothing, which is represented as... 

The field to be monitored is usually narrow and long in perimeter security applications. Thus, non-uniform deployment may be necessary. He et al. conclude that the sensor nodes generate false alarms at a non-negligible rate [18], and an exponentially weighted moving average on the sensor node is sufficient to eliminate transient alarms. 

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. ... 

The exponentially weighted moving average (EWMA) z k) is defined as... 

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. 

Holt, C. C. 1957. Forecasting seasonals and trends by exponentially weighted moving averages. Office of Naval Research, Arlington, VA, Report no. 52. 

Winters, P. R. 1960. Forecasting sales by exponentially weighted moving average. 

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