The diameter of a part produced by an automatic machine is a characteristic of interest. Based on historical data, the process average diameter is 15 mm with a process standard deviation of 0.8 mm. If samples of size 4 are randomly selected from the process:
(a) Find the 1σ and 2σ control limits.
(b) Find the 3σ control limits for the average diameter.
(c) What is the probability of a false alarm?
(d) If the process mean shifts to 14.5 mm, what is the probability of not detecting this shift on the first sample plotted after the shift? What is the ARL?
(e) What is the probability of failing to detect the shift by the second sample plotted after the shift?
(f) Construct the OC curve for this control chart.
(g) Construct the ARL curve for this control chart.