Question: You have an \(\bar{X}\) control chart set with UCL = 20 and LCL = 10. You take a sample of n = 4 units every half-hour. The mean of the process has historically been at 15, and the process standard deviation of the process has historically been 3.33.

a. If the mean shifts to 10, what is the probability of detecting the shift in the next sample?

b. How long, in hours, would you expect it to take for you to detect the shift?

c. What is the probability of not detecting the shift within 4 hours?