1. If Φ(-z0) = α/2, z0 = ? Assume α <0.1.
2. A company produces cooling tubes. The pressure of the tube is an important quality characteristic. Industrial standards require that the mean pressure must exceed 150 psi. The company wants to perform a hypothesis testing. Which of the following are the right hypotheses?
3. A decision rule is given here. Assume it applies to a normally distributed quality characteristic, the control chart has 3-sigma control limits, and the sample size is n=5.
Rule: If at least 2 out of the next 3 sample averages fall outside the control limits, conclude that the process is out of control.
What is the type II error of this rule? The β below is defined as follows: β = P(one sample average inside in the control limits | process out of control)
4. A process is controlled with a faction non-conforming control chart with three-sigma control limits, n=20. CL=0.10. What of the following answer is the closest to the width of the control limits?
(a) 0.1 (b) 0.2
(c) 0.3 (d) 0.4
(e) none of the above
5. Control charts for x' and R are in use with the following parameters:
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x' chart
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R chart
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UCL=363
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UCL=16.18
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CL=360
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CL=8.91
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LCL=357
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LCL=1.64
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The sample size is n=9. Both charts exhibit control. The quality characteristic is normally distributed.
(a) What is the α-risk associated with the x' chart?
(b) Suppose the mean shifts to 357. What is the probability that the shift will not be detected on the first sample following the shift?
(c) What would be the appropriate control limits for the x' chart if the type I error probability were to be 0.01?
6. In an x' chart, the following decision rule applies to a normally distributed quality characteristic with sample size n=4:
Rule: If at least one out of the next 3 sample averages fall outside 2-sigma control limits, conclude that the process is out of control.
If the mean of the quality characteristic does not change, but the process standard deviation doubles, what is the type II error of this rule?