Statistics for quantity: Control and Capability
Example of a typical process control technology.
• The software controls the laser, records measurements, makes the control charts, and sounds
an alarm when a point is out of control.
• This is typical of process control technology in modern manufacturing settings. Despite the
advanced technology involved, the software presents x and R charts rather than x and s charts,
no doubt because Prissier to explain.
• The R chart monitors within-sample variation (just like an s chart), so we look at it ﬁrst. We see
that the process spread is stable and well within the control limits. Just as in the case of s, the
LCL for R is 0 for the samples of size n=5 used here.
• The x chart is also in control, so process monitoring will continue. The software will sound an
alarm if either chart goes out of control.
Additional out-of-control rules
• 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 3σ 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. 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 rules.
• The most common step in this direction is to add a runs rule to the x chart.
• It is a mathematical fact that the runs rule responds to a gradual drift more quickly (on the
average) than the one-point-out rule does.