Looking at the graph of infection rates, my instincts told me that the process was stable as nothing about it looked nonrandom.  So I did some fact-checking, and the data certainly appears to fit the distributional assumption of geometric (and distribution fit is important for G and T Charts).  So then I took Dr. Wheeler's control limits, and calculated the odds of randomd data from that geometric distribution falling outside of the control limits - the result: 18.3%.  18.3%!  That's your false alarm rate.  He then circles 20% of the points and claims there is a lack of control.

If you think this is "a classic" then have fun chasing false alarms all day.  Apparently no research at all was done on the properties of the method he is proposing and as a statistician, I am deeply concerned about anyone reading this and blindly believing this is a better method.  As this method additionally requires calculations on your data, I do not see how it is easier either.

Further, the methods described for how standard G and T Charts are constructed are not common methods, and chances are very good that your statistical package uses a much better method and does not require the use of two different charts to detect shifts up and down.

If you have this type of data, check to see if it meets the distribution assumption of geometric or exponential (just a histogram should be a good enough check).  If it does, use the standard G or T Chart that Minitab or other packages provide.  If it does not then it is most likely more symmetric, in which case an I-MR Chart would work fine although you should ensure you have a posisitive LCL.

Use the method described in this article at your own peril.

Don - thank you for your reply to my comments.  This seems to be a chicken and egg situation.  If you assume data to be homogenous, then you may only detect a future issue that has deviated from the current homogenous state.  However, if the data were not homogenous to begin with, then this assumption may be masking signals.  So the best decision would seem to be to use some other knowledge to consider whether your assumption is reasonable or not.

In this case I would use two pieces of knowledge.  The first is that a Poisson process is known to have "opportunities between occurences" to be geometrically distributed.  In this case it may be reasonable to believe this is a Poisson process but we probably want other evidence as well.  Which would bring me to the second piece of knowledge which is the graph itself...removing centerline and control limits, the data simply look random.  As a practitioner, I would have serious doubts about the points labelled as out-of-control actually having special causes and would not waste time pursuing special causes for 20% of my points.

I have certainly read Shewhart's books and articles and understand he did not want control charts to be interpreted as fitted specific probabilities associated with the normal (or any other) distribution.  However, among all of the "example" datasets he uses, there is never a sample that comes out as skewed as data from time between events typically does.  They are all roughly "moundish".  I don't think considering data to have potentially come from a highly skewed distribution is rejecting Shewhart's ideas so much as evaluating an area in which Shewhart did not publish work.

In determing the best way to plot data from what we have good reason to believe is a highly-skewed distribution, the exponential or geometric distributions may not be perfect but they provide more reasonable limits than Shewhart's methods and only require one chart.  I find this to be much more useful and to provide more balanced and reasonable false alarm rates.

Also, I'm interested in investigating the methods you described for G- and T-Charts as they are not the ones I am familiar with.  Is there a reference I can consult for more information?  Your help would be greatly appreciated!