Two decision rules are given below based on seven consecutive samples. Assume they apply to a normally distributed quality characteristic. Further assume that the control chart has 3-sigma control limits. Rule 1: If one or more of the seven samples yield values of the test statistic that fall outside the control limits, conclude that the process is out of control.

Rule 2: If all of the seven samples fall on the same side of the center line, conclude that the process is out of control. (a) What is the overall Type I error probability of using rule 1 alone? (b) What is the overall Type I error probability of using rule 2 alone?