A production process making chemical solutions is in control when the solution strengths have a mean of μ0 = 0.650 and a standard deviation of σ = 0.015. Suppose that it is a reasonable approximation to take the solution strengths as being normally distributed. At regular time intervals the solution strength is measured and is plotted on a control chart.
(a) What are the center line and control limits of a 3-sigma control chart that you would construct to monitor the strengths of the chemical solutions?
(b) If a randomly sampled solution had a strength of x = 0.662, would you take this as evidence that the production process had moved out of control? What if x = 0.610?
(c) If the production process moves out of control so that the chemical solution strengths have a mean μ = 0.630 with σ = 0.015, what is the probability that a randomly sampled solution has a strength that lies outside the control limits? What is the average run length for detecting this change?