Suppose that a manager monitors both the X-bar and S-charts. The manager will stop the process if either a sample mean lies outside the control limits or a sample standard deviation lies outside the control limits. The control limits are set at ± 3 standard error bounds.
(a) By tracking both X-bar and S-charts, what is the probability of a Type I error?
(b) What assumption do you need in order to answer part (a)?