What is it: An EWMA (Exponentially Weighted Moving-Average) Chart is a control chart for variables data (data that is both quantitative and continuous in measurement, such as a measured dimension or time). The chart 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. As with other control charts, EWMA charts are used to monitor processes over time.
Why use it: Applies weighting factors which decrease exponentially. The weighting for each older data point decreases exponentially, giving much more importance to recent observations while still not discarding older observations entirely. The degree of weighing decrease is expressed as a constant smoothing factor α, a number between 0 and 1. α may be expressed as a percentage, so a smoothing factor of 10% is equivalent to α=0.1. Alternatively, α may be expressed in terms of N time periods, where . For example, N=19 is equivalent to α=0.1.
The observation at a time period t is designated Yt, and the value of the EMA at any time period t is designated St. S1 is undefined. S2 may be initialized in a number of different ways, most commonly by setting S2 to Y1, though other techniques exist, such as setting S2 to an average of the first 4 or 5 observations. The prominence of the S2 initialization's effect on the resultant moving average depends on α; smaller α values make the choice of S2 relatively more important than larger α values, since a higher α discounts older observations faster.
The advantage of EWMA 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.
Where to use it: 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.
When to use it: EWMA (or Exponentially Weighted Moving Average) 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.
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. An 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.
How to use it: Interpreting an EWMA Chart 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.
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.
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.