... within on day 10)=0.95100.60

Hence, the probability that at least one mean lies outside the control limits is 1 − 0.60 = 0.40. The chance of a Type I error during 10 days is larger than the chance on any one day. A 5% chance for a Type I error on any one day implies there is a 40% chance for a Type I error during 10 days. Repeated testing eventually signals a problem. Testing the process for 25 consecutive days increases the chance that a Type I error will occur during this period to 1 − 0.9525 ≈ 0.72.

Smaller values of α reduce the chance of a Type I error but at a cost. Reducing α moves the control limits farther from μ, increasing the chance ...

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