Quality and Reliability Methods - SAS

98 Cumulative Sum Control Charts Chapter 6
Cumulative Sum (Cusum) Charts
• On a Shewhart control chart, horizontal control limits define whether a point signals an out-of-control
condition. On a cusum chart, the limits can be either in the form of a V-mask or a horizontal decision
interval.
• The control limits on a Shewhart control chart are commonly specified as 3σ limits. On a cusum chart,
the limits are determined from average run length, from error probabilities, or from an economic design.
A cusum chart is more efficient for detecting small shifts in the process mean. Lucas (1976) comments that
a V-mask detects a 1σ shift about four times as fast as a Shewhart control chart.
Launch Options for Cusum Charts
When you choose Analyze > Quality And Process > Control Chart > Cusum, the Control Chart launch
dialog appears, including appropriate options and specifications as shown here.
Figure 6.3 Cusum Chart Launch Options
Two Sided
Data Units
See “Parameters” on page 32 in the “Statistical Control Charts” chapter for a description of K Sigma. The
following items pertain only to cusum charts:
Requests a two-sided cusum scheme when checked. If it is not checked, a one-sided scheme is used and no
V-mask appears. If an H value is specified, a decision interval is displayed.
Specifies that the cumulative sums be computed without standardizing the subgroup means or individual
values so that the vertical axis of the cusum chart is scaled in the same units as the data.
Note: Data Units requires that the subgroup sample size be designated as constant.
H
H is the vertical distance h between the origin for the V-mask and the upper or lower arm of the V-mask for
a two-sided scheme. You also enter a value for the increase in the lower V-mask per unit change on the
subgroup axis (Figure 6.2). For a one-sided scheme, H is the decision interval. Choose H as a multiple of the
standard error.