Suppose that a manager monitors both the -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...

Suppose that a manager monitors both the
-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
 standard error bounds.

(a) By tracking both
-bar and
-charts, what is the probability of a Type I error?

(b) What assumption do you need in order to answer part (a)?