Solved: Consider a control chart for individuals, applied to a continuous 24-hour

Chapter 16, Problem 16-50

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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 ARL 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 ? (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.

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