## 6.05.2011

### Statistical Process Control - EWMA Charts

What is a EWMA Chart?
A EWMA Chart is a control chart for variables data (data that is both quantitative and continuous in measurement, such as a measured dimension or time). It plots weighted moving average values. A weighting factor is chosen by the user to determine how older data points affect the mean value compared to more recent ones. Because the EWMA Chart uses information from all samples, it detects much smaller process shifts than a normal control chart would.

Although standard EWMA charts are designed to monitor processes with a stable mean, a modified EWMA control charts may be used for auto correlated processes with a slowly drifting mean.

When to Use a EWMA Charts?
EWMA Charts are generally used for detecting small shifts in the process mean. They will detect shifts of .5 sigma to 2 sigma much faster than Shewhart charts with the same sample size. They are, however, slower in detecting large shifts in the process mean. In addition, typical run tests cannot be used because of the inherent dependence of data points.

EWMA Charts may also be preferred when the subgroups are of size n=1. In this case, an alternative chart might be the Individual X Chart, in which case you would need to estimate the distribution of the process in order to define its expected boundaries with control limits. The advantage of Cusum, EWMA and Moving Average charts is that each plotted point includes several observations, so you can use the Central Limit Theorem to say that the average of the points (or the moving average in this case) is normally distributed and the control limits are clearly defined.

When choosing the value of lambda used for weighting, it is recommended to use small values (such as 0.2) to detect small shifts, and larger values (between 0.2 and 0.4) for larger shifts. A EWMA Chart with lambda = 1.0 is an X-bar Chart.

EWMA charts are also used to smooth the affect of known, uncontrollable noise in the data. Many accounting processes and chemical processes fit into this categorization. For example, while day to day fluctuations in accounting processes may be large, they are not purely indicative of process instability. The choice of lambda can be determined to make the chart more or less sensitive to these daily fluctuations.

As with other control charts, EWMA charts are used to monitor processes over time. The charts' x-axes are time based, so that the charts show a history of the process. For this reason, you must have data that is time-ordered; that is, entered in the sequence from which it was generated. If this is not the case, then trends or shifts in the process may not be detected, but instead attributed to random (common cause) variation.

Interpreting an EWMA Chart
a) Standard Case (Non-wandering Mean)
Always look at Range chart first. The control limits on the EWMA chart are derived from the average Range (or Moving Range, if n=1), so if the Range chart is out of control, then the control limits on the EWMA chart are meaningless

On the Range chart, look for out of control points. If there are any, then the special causes must be eliminated. Remember that the Range is the estimate of the variation within a subgroup, so look for process elements that would increase variation between the data in a subgroup. Brainstorm and conduct Designed Experiments. Note that Auto Drop is not invoked for EWMA charts.

After reviewing the Range chart, interpret the points on the EWMA chart relative to the control limits. Run Tests are never applied to a EWMA chart, since the plotted points are inherently dependent, containing common points. Never consider the points on the EWMA chart relative to specifications, since the observations from the process vary much more than the Exponentially Weighted Moving Averages.

If the process shows control relative to the statistical limits for a sufficient period of time (long enough to see all potential special causes), then we can analyze its capability relative to requirements. Capability is only meaningful when the process is stable, since we cannot predict the outcome of an unstable process.

b) Wandering Mean Chart
Look for out of control points. These represent a shift in the expected course of the process, relative to its past behavior. The chart is not very sensitive to subtle changes in a drifting process, since it accepts some level of drift as being the nature of the process. Remember that the control limits are based on an exponentially smoothed prediction error for past observations, so the larger the prior drifts, the more insensitive the chart will be to detecting changes in the amount of drift.

Here is an example of how a EWMA chart looks, with trends and special causes identified: TeraSigma is capable to perform EWMA charts for specific processes. Let us know your need and we’ll be glad to collaborate on your project.