Suppose that when a process is in control a variable can be taken to be normally distributed with a mean of μ0 = 10.0 and a standard deviation of σ = 0.2, and that a control chart is to be implemented by plotting the average of n = 4 observations at each time point.
(a) What are the center line and control limits of a 3-sigma control chart that you would construct to monitor this process?
(b) If a sample average  = 9.5 is obtained, should the process be declared to be out of control? What if  = 10.25?
(c) If the process moves out of control so that the variable mean becomes μ = 10.15 with σ = 0.2, what is the probability that an observation lies outside the control limits? What is the average run length for detecting this change?