## Cusum Charts Compared with Shewhart Charts

Although cusum charts and Shewhart charts are both used to
detect shifts in the process
mean, there are important differences in the two methods.
- Each point on a Shewhart chart is based on information for a
single subgroup sample or measurement. Each point on a cusum
chart is based on information from all samples (measurements) up
to and including the current sample (measurement).
- On a Shewhart chart, upper and lower control limits are used to
decide whether a point signals an out-of-control condition. On
a cusum chart, the limits take the form of a decision interval
or a V-mask.
- On a Shewhart chart, the control limits are commonly computed as
3 limits. On a cusum chart, the limits are determined
from average run length specifications, specified error
probabilities, or an economic design.

A cusum chart offers several advantages over a Shewhart chart.

- A cusum chart is more efficient for detecting small shifts in
the process mean, in particular, shifts of 0.5 to 2 standard
deviations from the target mean (refer to Montgomery 1996).
Lucas (1976) noted that "a V-mask designed to detect a
shift will detect it about four times as fast as a
competing Shewhart chart."
- Shifts in the process mean are visually easy to detect on a cusum
chart since they produce a change in the slope of the plotted
points. The point at which the slope changes is the point at
which the shift has occurred.

These advantages are not as pronounced if the Shewhart chart is
augmented by the tests for special causes described by Nelson (1984,
1985). Also see Chapter 48, "Tests for Special Causes."
Moreover,

- cusum schemes are more complicated to design.
- a cusum chart can be slower to detect large shifts in the
process mean.
- it can be difficult to interpret point patterns on a cusum chart
since the cusums are correlated.

Copyright © 1999 by SAS Institute Inc., Cary, NC, USA. All rights reserved.