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Lecture 14

ECON 2500 Lecture 14: Chapter 17 Statistics for quantity Control and Capability Lecture 14

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ECON 2500
Andrei Semenov

Chapter 17 Statistics for quantity: Control and Capability Lecture 14 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.
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