12.27 Additional out-of-control signals.

A single extreme point outside of three-sigma limits represents one possible statistical signal of unusual process behavior. As we saw with Figure 12.5(a) (page 608), process change can also give rise to unusual variation within control limits. A variety of statistical rules, known as runs rules, have been developed to supplement the three-sigma rule in an effort to more quickly detect special cause variation. A commonly used runs rule for the detection of smaller shifts of gradual process drifts is to signal if nine consecutive points all fall on one side of the center line. We have learned that for an in-control process and the assumption of Normality, the false alarm rate for the three-sigma rule is about three in 1000. Assuming Normality of the control chart statistics, what is the false alarm rate for the nine-in-a-row rule if the process is in control?