A process has a target of 0  100 and a standard deviation of  4.

Samples of size n  1 are taken every two hours. Use Table 15-9.

(a) Suppose the process mean shifts to  102.

How many hours of production will occur before the process shift is detected by a CUSUM with h  5 and k  12?

(b) It is important to detect the shift defined in part

(a) more quickly. A proposal is made to reduce the sampling frequency to 0.5 hour. How will this affect the CUSUM control procedure? How much more quickly will the shift be detected?

(c) Suppose that the 0.5 hour sampling interval in part

(b) is adopted. How often will false alarms occur with this new sampling interval? How often did they occur with the old interval of two hours?

(d) A proposal is made to increase the sample size to n  4 and retain the two-hour sampling interval. How does this suggestion compare in terms of average detection time to the suggestion of decreasing the sampling interval to 0.5 hour?