A process is normally distributed and in control, with known mean and variance,

Question

A process is normally distributed and in control, with known mean and variance, and the usual three-sigma limits are used on ?? 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 limits when m=5? Repeat these calculations for the cases where m = 10, m= 20 and m=30. Discuss the results that you have obtained.

Explanation / Answer

Use Binomial Distribution function formula and use m=5,10... asn=5, 10.

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