Two decision rules are given here. Assume they apply to normally distributed qua
ID: 3204659 • Letter: T
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. Rule 1: If one or more of the next eight samples yield values of the sample average that fall outside the control limits, conclude that the process is out of control. Rule 2: 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
Answer:
We know that the type I error probability is the probability of rejecting the null hypothesis H0 when it is true.
Type I error probability for the first rule is given as below:
Null hypothesis: H0: One of more of the next eight samples yield values of the sample average that fall inside the control limits.
Alternative hypothesis: Ha: One of more of the next eight samples yield values of the sample average that fall outside the control limits.
The type I error probability for the first rule is the probability of rejecting the null hypothesis that the process is in control however actually process is in control. We reject the hypothesis that the one or more of the next eight samples yield values of the sample average that fall inside the control limits however actually values inside the control limits, then the type I error occurred.
Type I error probability for the second rule is given as below:
Null hypothesis: H0: Next eight sample averages do not fall on the same side of the centre line.
Alternative hypothesis: Ha: Next eight sample averages fall on the same side of the centre line.
The type I error probability for the second rule is the probability of rejecting the hypothesis that next eight sample averages do not fall on the same side of the centre line, however actually eight sample averages do not fall on the same side of the centre line.
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