November 2003 Vol. 5, No. 11
 Quality Quiz from Professor Cleary 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.