Vol. 5, No. 11

Congratulations! 
You're right!

Tabby should be happy, since LaMal’s theory is dead wrong. 
Control limits become wider because of the A2 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 A₂ 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 A₂value 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 become 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 the documentation for SQCpack 2000. By clicking here http://www.sqcpack.com/support.htm, you will find a link to this documentation. Refer to pages 302-304.