CHAPTER 27 • Statistical Process Control

27-14 CHAPTER 27 • Statistical Process Control
plotted for Sample 1. The center line is at 275 mV. The upper and lower
control limits are
s
m 3
2n 275 3 43
275 64.5 339.5 mV
24
(UCL)
s
m 3
2n 275 3 43
275 64.5 210.5 mV
24
(LCL)
As is common, we have labeled the control limits UCL for upper control limit
and LCL for lower control limit.
EXAMPLE 27.4 Interpreting x charts
Figure 27.4(b) is a typical x chart for a process in control. The means of the 20 samples
do vary, but all lie within the range of variation marked out by the control limits. We
are seeing the common cause variation of a stable process.
Figures 27.5 and 27.6 illustrate two ways in which the process can go out of control.
In Figure 27.5, the process was disturbed by a special cause sometime between Sample
12 and Sample 13. As a result, the mean tension for Sample 13 falls above the upper
control limit. It is common practice to mark all out-of-control points with an “x” to
call attention to them. A search for the cause begins as soon as we see a point out of
control. Investigation finds that the mounting of the tension-measuring device had
slipped, resulting in readings that were too high. When the problem was corrected,
Samples 14 to 20 were again in control.
Figure 27.6 shows the effect of a steady upward drift in the process center, starting at
Sample 11. You see that some time elapses before the x for Sample 18 is out of control.
Process drift results from gradual changes such as the wearing of a cutting tool or overheating.
The one-point-out signal works better for detecting sudden large disturbances
than for detecting slow drifts in a process. ■
400
350
UCL
x
Sample mean
300
250
FIGURE 27.5
This x chart is identical to that in
Figure 27.4(b) except that a special
cause has driven x for Sample 13
above the upper control limit. The
out-of-control point is marked with
an x.
200
150
LCL
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Sample number