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 Rbar 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 Rbar 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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