Chapter 12 Quality Control 509
As shown in Figure 12-14, the lower control limit is 0.01069, or a defect
percentage of about 1%. The upper control limit is 0.11281, or about 11%.
The average defect percentage is 0.06175, about 6%. The control chart clearly
demonstrates that no point is anywhere near the 3-s limits.
Note that not all out-of-control points indicate the existence of a problem.
For example, suppose that another sample of 200 rods was taken and that
only one rod failed the stress test. In other words, only one-half of 1% of the
sample was defective. In this case, the proportion is 0.005, which falls be-
low the lower control limit, so technically it is out of control. Yet you would
not be concerned about the process being out of control in this case, because
the proportion of defects is so low. Still, you might be inclined to investi-
gate, just to see whether you could locate the source of your good fortune
and then duplicate it!
You can save and close the Steel Control Chart workbook now.
Control Charts for Individual Observations
Up to now, we’ve been creating control charts for processes that can be
neatly divided into subgroups. Sometimes it’s not possible to group the data
into subgroups. This could occur when each measurement represents a sin-
gle batch in a process or when the measurements are widely spaced in time.
With a subgroup size of 1, it’s not possible to calculate subgroup ranges.
This makes many of the regular formulas impractical to apply.
Instead, the recommended method is to create a subgroup consisting of
each consecutive observation and then calculate the moving average of the
data. Thus the subgroup variation is determined by the variation from one
observation to another, and that variation will be used to determine the con-
trol limits for the variation between subgroups. Because we are setting up
our subgroups differently, the formulas for the lower and upper control lim-
its are different as well. The LCL and UCL are
LCL 5 x 23 R
d 2
UCL 5 x 13 R
d 2
Here x is the sample average of all of the observations, R is the average
range of consecutive values in the data set, and d 2 is the control limit fac-
tor shown earlier in Table 12-3. We are using a moving average of size 2, so
this will be equal to 1.128. Control charts based on these limits are called
individuals charts.
