Paul,

Well....not as simple as you think.

The "proper" calculation for control limits use an average (local)  dispersion statistics not the global formula you suggest. This use of a local statistic minimizes the effect of out-of -contol points on the limits. As Wheeler says: You get Good Limits from Bad Data.

Read Wheeler....and then read him again.

Rich DeRoeck 

Be prepared for questions when people ask you, "Why don't I get the same limits as Minitab?" -- because one should never use the "typical" calculation of standard deviation for control limits, which is what you describe (As I say to people I teach regarding that, "What part of 'never' don't you understand?").  If there are special causes, as there seem to be in your data, this estimate will be inflated, sometimes seriously.

Given the way you describe the data collection, there are also a couple of different ways you could calculate it -- Wheeler has discussed this in his many "rational subgrouping" columns.

And your alleged special cause -- Point 7 is indeed below the limit.  Maybe it isn't even the special cause.  Rather than that one point below the limit, one should investigate a possible process shift that seems to settle in around observations 16-17.  This SHIFT might be the special cause and Point 7 could actually be common cause before the shift took place!  That said...

...I'd also be concerned about points 5 and 6, which could be a special cause in "process 1" -- as could points 21 and 22 in "process 2."  With the data, one could see whether the moving ranges from point 4 to 5 and point 6 to 7 might be suspect...as might the moving ranges from  20 to 21 and 22 to 23.  You get the idea -- it's not just as simple as calculating limits and looking for points outside the limits.

And if you sub-grouped the data (a possibility given the way you collected it), then the moving range isn't appropriate.  BUT...calculating the standard deviation correctly, THAT is what might flag points 5 and 6 and 21 and 22 as special causes (outside the limits) with their appropriate center lines if the shift is confirmed. 

I appreciate what you're trying to do in these columns on the tools, but I just couldn't let these (relatively) common teaching errors about calculating the standard deviation or interpretation get a free pass.

Just goes to show you, a statistician's favorite answer is, "It depends."  If only it were so simple.  Rather than teach people tools, we should try to teach them how to ask better questions to change conversations.

Davis Balestracci

Paul, I will not be as polite and diplomatic as my good friend Davis. Regarding your calculation of control limits, you are COMPLETELY WRONG!!! You mention Shewhart's work, but obviously did not learn much from it. Have you read the book? Your data is time-ordered. The SD calculation has nothing to do with time order. The SD will be the same value regardless of the order of the data. That alone should be a clue that SD is not the proper statistic to calculate control limits. An "average dispersion statistic" (i.e., average moving range) must be used with the proper bias factor. SD is an enumerative calculation, while a control chart is an analytic tool. There is a huge difference between "enumerative" and "analytical" studies. This concept was well-documented by Deming. Whatever Improvement Ninja level you possess, please demote yourself by two belts, Grasshopper. Your data obviously shows a shift - another clue. So, calculating control limits the proper way from all the data does not complete the analysis. In fact, the Mean and Control Limits for such an out-of-control situation are, in fact, meaningless! The system is obviously not showing a "reasonable degree of statistical control" and should be split into at least two separate periods and the limits recalculated (properly) for each. I'll stop now, before I hyperventilate. Sorry if I seem harsh, but you need to properly educate yourself before writing articles for public view.