Consider a control chart for individuals applied to a continuous 24-hour chemical process with observations taken every hour.

(a) If the chart has 3-sigma limits, verify that the in-control ARL is 370. How many false alarms would occur each 30-day month, on the average, with this chart?

(b) Suppose that the chart has 2-sigma limits. Does this reduce the ARL for detecting a shift in the mean of magnitude σ? (Recall that the ARL for detecting this shift with 3-sigma limits is 43.9.)

(c) Find the in-control ARL if 2-sigma limits are used on the chart. How many false alarms would occur each month with this chart? Is this in-control ARL performance satisfactory? Explain your answer.