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Quality Quiz:Professor Cleary
Another quiz from Professor Cleary

Congratulations: "B" is correct!

Tabby should be happy, since Cora’s theory is dead wrong. 

Control limits become wider because of the value used to calculate them, and the R-bar changes, not because of variability within the sample.

Sample #8 has a sample size of 5. The calculation of control limits for that sample (and all other samples with a size of 5) follows. The proper  value when n = 5 is .577.

Sample #9 has a sample size of 2. The control limits are wider than those of Sample #8. The proper  value when n = 2 is 1.88.

It is also to be noted that the R-bar changes as the sample size changes.

It is easy to see in this example that when the sample size becomes smaller, the control limits becomes wider. A logical explanation is that with a smaller sample, the estimate of the mean is less likely to be accurate, so control limits must become wider. On the other hand, with a larger sample—say, 10—the control limits would be tighter because of more accurate prediction of the mean.

For a more detailed explanation, refer to Practical Tools for Continuous Improvement.


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