Question

A process is normally distributed and in control, with known mean and variance, and the usual 3 sigma limits are used on the ?̅ control chart, so that the probability of a single point plotting outside the control limits when the process is in control is 0.0027. Suppose that this chart is being used in Phase 1 and the averages from a set of M samples or subgroups from this process are plotted on this chart. What is the probability that at least one of the averages will plot outside the control limit when M = 5? Repeat these calculations from the cases where M = 10, M = 20, M = 30, M = 50. Discuss the results that you have obtained.

Answer 1