Cumulative Sum charts, or Cusum charts, are
an alternative to Shewhart control charts. While
Shewhart control charts are widely used and
the control violations well documented, there
may be conditions to which they are insensitive.
This technique determines an average value for
the subgroups and determines the expected variability
about the mean. These charts are good at detecting
distinct, steady and intermittent shifts in
the process.
Cusum charts are better suited to detecting
small, sustained shifts in a process. These
charts measure a cumulative deviation from the
mean or a target value. The chart, therefore,
displays the deviation from the target instead
of the rate or mean value of the subgroup size,
which is what is plotted on a Shewhart chart.
If the process remains in control, then the
deviations will scatter around the target or
average value. On the Cusum chart, this will
produce a straight line or a random shift around
the target with a mean of zero.
There is another significant difference in
a Cusum chart, which is the accumulation of
the deviations. This is what gives this technique
its name. Each point on a Cusum chart is based
on information from all samples, including the
current sample. The plotted points represent
the cumulative deviations from the target value.
If the deviations from the target fluctuate
in opposite directions about the target, including
large fluctuations, the Cusum chart may not
provide adequate indication of process problems.
This is due to the fact that it is charting
cumulative deviations. If the deviations are
both above and below target, it will not result
in an increasing or decreasing trend. Instead,
it will show that the process is centering around
the mean or target. However, if there is a consistent
increasing or decreasing trend, the Cusum chart
will be much more sensitive to this than Shewhart
charts. The detection of trends holds true even
with small shifts. Cusum charts are better at
detecting trends in process shifts between .5
and 2 sigma. Shewhart techniques typically identify
larger shifts in the process. The larger shifts
are more likely to be identified by Shewhart
charts regardless of whether they are sporadic
or a trend.
Here is a comparison of a U-Chart and a Cusum
chart for data on medication errors. In this
example, medication errors are charted against
total doses administered. Since multiple errors
could occur during the administration of a single
dose, it is appropriate to use a U-chart rather
than a P-chart. A single dose could be a combination
of the incorrect amount, the wrong medication,
administered improperly, administered to the
wrong patient, etc. Although this distinction
is subtle, it is important. However, chart choice
is a subject for another article. This purpose
here is to illustrate the value of Cusum charts.
The U-type Cusum chart for this data is show
below. The last 13 months of 24 months of medication
errors are plotted. The first 5 months of this
period show that there is little cumulative
deviation from the target value of 0. After
that period, however, there appears to be an
increasing trend in medication errors. What
does this look like on the U-chart?
The U-chart for the same time period shows
a control violation in the 22nd month. Although
the control violation would need to be investigated,
there is no substantial indication of an upward
trend in medication errors in this chart. With
the exception of 1point, this chart describes
a process that is experiencing normal variation.
Mouse over any data point or other "hot
spot" to view additional information
In conclusion, there may be multiple tools
that should be employed to more completely characterize
a process. Any chart should be used with discretion.
Even in the absence of control violations, charts
should be scrutinized to determine if the results
are reasonable. In the U-chart example, perhaps
the variability is an issue that warrants further
investigation. The cumulative variability does
show a trend when viewed in the Cusum context.
