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When to Use an EWMA Chart
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. 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. 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.
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.
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.
See also:
Autocorrelation
Charts
CuSum
Charts
Moving
Average / Range Chart
Moving
Average / Sigma Chart
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