Interpretation & Calculations
As with other control charts, EWMA (or Exponentially Weighted Moving Average) Charts are used to monitor processes over time. The 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.
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 (i.e. X-Bar charts and Individual-X charts) with the same sample size. They are, however, slower in detecting large shifts in the process mean. In addition, typical run test rules cannot be used because of the inherent dependence of data points. When not available, a Moving Average chart such as offered in our SPC software provides similar benefits.
EWMA Charts may also be preferred when the subgroup size is 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 chart 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. An EWMA Chart with lambda = 1.0 is an X-Bar chart (or an Individual-X chart when the subgroup size is one.
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. Here again, a Moving Average chart such as offered in our SPC software is a bit easier to use, as its moving cell width can be set to the number of days for a particular cycle (e.g. set to 7 for one plotted point a week if data exists for seven days).
A modified EWMA control charts may be used for autocorrelated processes with a slowly drifting mean. The wandering mean case has been presented by Montgomery and Mastrangelo (Journal of Quality Technology, July 1991, vol. 23, No. 3, pp. 179-193) for processes that are positively autocorrelated and the mean does not drift too fast. Subgroup size for the wandering mean case is limited to n=1, since the subgroup range would not provide a meaningful indicator of process variation when observations are autocorrelated. See EWMA Forecast
Learn more about the SPC principles and tools for process improvement in Statistical Process Control Demystified (2011, McGraw-Hill) by Paul Keller, in his online SPC Concepts short course (only $39), or his online SPC certification course ($350) or online Green Belt certification course ($499).