ANSWER:Oops. There goes the black belt in Dinah's future.
She'll have to aspire to some other fashion statement, if she hopes to impress her boss with her statistical knowledge. It's clear that she does not know why the variation in control limits occurs.
When Shewhart introduced X-bar and R charts, it was not because they represented the most statistically efficient approach, but rather because they are mathematically easier to create. When PQ Systems' original SQCpack was created by Sean Cleary in 1982 at the age of 15, I felt as a statistician, that X-bar and S charts would soon have standard use, since computers can create them as easily as X-bar and R charts. What I did not take into consideration, however, was the power of tradition in determining usage. Grant and Leavenworth and other statisticians including myself continued to promote the application of X-bar and R charts, and as a result they have maintained their general usage in SPC. Indeed, the approach is robust enough to be useful to most applications, but in the meantime the potential offered by X-bar and S charts has been largely overlooked.
It is true that control limits on the S portion of X-bar and S charts vary. At least, sometimes they do, and sometimes they don't. So Dinah Thyrst was right in this respect. Understanding the reasons for the variation in control limits is an entirely new question to ponder, however.
-Ponderous Puzzlers cleverly thought up by Michael J. Cleary, Ph.D. and Barb Cleary, PQ Systems Inc.