Rather than stop the production when a mean crosses the control limits in the X 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 2 n (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

Question: Rather than stop the production when a mean crosses the control limits in the X-bar chart, a manager has decided to wait until two consecutive

Rather than stop the production when a mean crosses the control limits in the X-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 μ ± 2σ / √n.
(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?

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