Two decision rules are given here. Assume the rules apply to a normally distributed quality characteristic, the control chart has three-sigma control limits, and the sample size is n=6. 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 six sample averages fall on the same side of the center line, 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, what is the Type-II error probability associated with each decision rule? (c) What is the combined (overall) Type-I error for these rules? (One can assume independence for these rules only for the in-control process.)