Quality and Reliability Methods - SAS

Chapter 6 Cumulative Sum Control Charts 97
Cumulative Sum (Cusum) Charts
Cumulative Sum (Cusum) Charts
Cumulative Sum (Cusum) charts display cumulative sums of subgroup or individual measurements from a
target value. Cusum charts are graphical and analytical tools for deciding whether a process is in a state of
statistical control and for detecting a shift in the process mean.
JMP cusum charts can be one-sided, which detect a shift in one direction from a specified target mean, or
two-sided to detect a shift in either direction. Both charts can be specified in terms of geometric parameters
(h and k shown in Figure 6.2); two-sided charts allow specification in terms of error probabilities α and β.
To interpret a two-sided Cusum chart, you compare the points with limits that compose a V-mask. A
V-mask is formed by plotting V-shaped limits. The origin of a V-mask is the most recently plotted point,
and the arms extended backward on the x-axis, as in Figure 6.2. As data are collected, the cumulative sum
sequence is updated and the origin is relocated at the newest point.
Figure 6.2 Illustration of a V-Mask for a Two-Sided Cusum Chart
upper arm
vertex
lower
arm
d
h, the rise in the arm
corresponding to the distance (d)
from origin to vertex
1 unit
k, the rise in the arm
corresponding to one
sampling unit
Shifts in the process mean are visually easy to detect on a cusum chart because they produce a change in the
slope of the plotted points. The point where the slope changes is the point where the shift occurs. A
condition is out-of-control if one or more of the points previously plotted crosses the upper or lower arm of
the V-mask. Points crossing the lower arm signal an increasing process mean, and points crossing the upper
arm signal a downward shift.
There are major differences between cusum charts and other control (Shewhart) charts:
• A Shewhart control chart plots points based on information from a single subgroup sample. In cusum
charts, each point is based on information from all samples taken up to and including the current
subgroup.