CHAPTER 27 • Statistical Process Control

27-24 CHAPTER 27 • Statistical Process Control
x and R charts, remember that the interpretation of these charts is just like the
interpretation of x and s charts.
Additional out-of-control signals. So far, we have used only the basic “one
point beyond the control limits” criterion to signal that a process may have gone
out of control. We would like a quick signal when the process moves out of control,
but we also want to avoid “false alarms,” signals that occur just by chance
when the process is really in control. The standard 3 control limits are chosen to
prevent too many false alarms, because an out-of-control signal calls for an effort
to find and remove a special cause. As a result, x charts are often slow to
respond to a gradual drift in the process center that continues for some time
before finally forcing a reading outside the control limits. We can speed the
response of a control chart to lack of control—at the cost of also enduring more
false alarms—by adding patterns other than “one-point-out” as signals. The most
common step in this direction is to add a runs signal to the x chart.
OUT-OF-CONTROL SIGNALS
x and s or x and R control charts produce an out-of-control signal if:
■ One-point-out: A single point lies outside the 3 control limits of either chart.
■ Run: The x chart shows 9 consecutive points above the center line or 9 consecutive
points below the center line. The signal occurs when we see the 9th point of the run.
EXAMPLE 27.7 Using the runs signal
Figure 27.11 reproduces the x chart from Figure 27.6. The process center began a
gradual upward drift at Sample 11. The chart shows the effect of the drift—the sample
400
x
x
350
UCL
x
Sample mean
300
250
x
200
LCL
FIGURE 27.11
x chart for mesh tension data when
the process center drifts upward. The
“run of 9” signal gives an out-of-control
warning at Sample 17.
150
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Sample number