Two decision rules are given here. Assume they apply to normally distributed qua

Question

Two decision rules are given here. Assume they apply to normally distributed quality characteristic, the control chart has three-sigma control limits, and the sample size is n = 5. If one or more of die next eight samples yield values of the sample average that fall outside the control limits, conclude that the process is out of control. If all of the next eight sample averages fall on the same side of die center line, conclude that the process is out of control. What is the type I error probability for each of these rules?

Explanation / Answer

Type-I error is if all of the next eight samples yield values of the sample mean that fall inside the control limits. But the researcher concludes that the process is out of control.

Type-I error is if all of the next eight samples yield values of the sample mean that fall inside the control limits. But the researcher concludes that the process is out of control.

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