Question 12.60

12.60 Even more signals.

There are other out-of-control signals that are sometimes used with charts. One is “15 points in a row within the level.” That is, 15 consecutive points fall between and . This signal suggests either that the value of used for the chart is too large or that careless measurement is producing results that are suspiciously close to the target. Find the probability that the next 15 points will give this signal when the process remains in control with the given and .