2.
Measurement Process Characterization
2.2.
Statistical control of a measurement process
2.2.2.
How are bias and variability controlled?
2.2.2.1.
Shewhart control chart
2.2.2.1.1.
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EWMA control chart
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Small changes only become obvious over time
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Because it takes time for the patterns in the data to emerge, a
permanent shift in the process may not immediately cause individual
violations of the control limits on a Shewhart control chart.
The Shewhart control chart is not powerful
for detecting small changes, say of the order of 1 - 1/2 standard
deviations. The EWMA (exponentially weighted moving average) control
chart is better suited to this purpose.
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Example of EWMA control chart
for mass calibrations
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The exponentially weighted moving average (EWMA) is a statistic for
monitoring the process that averages the data in a way that gives less
and less weight to data as they are further removed in time from the
current measurement. The data
are the check standard measurements ordered in time. The EWMA statistic
at time t is computed recursively from individual data points,
with the first EWMA statistic, EWMA1, being the arithmetic
average of historical data.
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Control mechanism for EWMA
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The EWMA control chart can be made sensitive to small changes or a
gradual drift in the process by the choice of the weighting factor,
 . A weighting factor of
0.2 - 0.3 is usually suggested for this purpose
(Hunter), and 0.15 is also a
popular choice.
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Limits for the control chart
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The target or center line for the control chart is
the average of historical data. The upper (UCL) and lower (LCL) limits
are
where s times the radical expression is a good approximation to
the standard deviation of the EWMA statistic and the factor k is
chosen in the same way as for the Shewhart control chart -- generally
to be 2 or 3.
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Procedure for implementing the EWMA control chart
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The implementation of the EWMA control chart is the same as for any
other type of control procedure. The procedure is built on the
assumption that the "good" historical data are representative of the
in-control process, with future data from the same process tested for
agreement with the historical data. To start the procedure, a target
(average) and process standard deviation are computed from historical
check standard data. Then the procedure enters the
monitoring stage with the EWMA statistics
computed and tested against the control limits. The EWMA statistics
are weighted averages, and thus their standard deviations are smaller
than the standard deviations of the raw data and the corresponding
control limits are narrower than the control limits for the Shewhart
individual observations chart.
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