Rather than stop the production when a mean crosses the control limits in the -bar chart, a manager has decided to wait until two consecutive means lie outside the control limits before stopping the...

Rather than stop the production when a mean crosses the control limits in the
-bar chart, a manager has decided to wait until two consecutive means lie outside the control limits before stopping the process. The control limits are at
.

(a) By waiting for two consecutive sample means to lie outside the control limits, has the manager increased or decreased the chance for a Type I error?

(b) What is the probability of a Type I error if this procedure is used?