Two decision rules are given here. Assume they apply to a normally distributed quality characteristic, the control chart has three-sigma control limits, and the sample size is n=5.

Rule 1: If one or more of the next seven samples yield values of the sample average that fall outside the control limits, conclude that the process is out of control.

Rule 2: If all of the next seven sample averages fall on the same side of the centerline, conclude that the process is out of control.

a) What is the Type-I error probability for each of these rules?

b) If the mean of the quality characteristic shifts one process standard deviation, and remains there during the collection of the next seven samples, what is the Type-II error probability associated with each decision rule?