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When
to Use a Cu Sum Chart
Cu Sum (or Cumulative Sum)
Charts are generally used for detecting small shifts in the process mean.
They will detect shifts of .5 sigma to 2 sigma in about half the time of
Shewhart charts with the same sample size (Montgomery 1991). The point at
which shifts occur is easy to detect by an inflection in the plotted points.
They are, however, slower in detecting large shift in the process mean.
In addition, typical run tests cannot be used because of the dependence
of data points.
Cu Sum 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 Cu Sum, 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.
As with other control
charts, Cu Sum 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
EWMA
Charts
Moving
Average / Range Chart
Moving
Average / Sigma Chart
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