Thanks, Davis, I liked this for several reasons. Software gives us many rules, and evaluates them with the click of a mouse. Wheeler and Chambers demonstrated a number of years ago that the four primary WE Zone tests (1, 2, 3 and 4—1, 2, 5 and 6 for Minitab and JMP) offer the best trade-off between finding signals that are there and tampering by reacting to false signals. When using software, I generally use one other rule with XbarR or XbarS charts (in Minitab, it’s test 7)…15 points within one sigma of the center line. This doesn’t indicate special cause; it just tells you that you’re subgrouping unlike things. Bill Woodall mentioned offhandedly, at the 2001 FTC here in Minneapolis, that “of course, no statistician uses the trend rule in control charting.” I still see it often, though.

Great point about plotting the dots, too. Deming once did a lecture series for Ford statisticians (Bill Scherkenbach has the transcripts and shared them with me). This conversation always stuck with me:

“DR DEMING:  I'll tell you a couple of tools that I find to be useful. One is a piece of paper, and another was a pencil. And almost nobody has those tools on hand.  To save his soul from hell, he won't use them. He's gotta do it by computer, or some statistical test.

“Had some data. I can't call them clients…They had troubles. Asked if they'd collect some data on beginning, middle, and end of several batches...hardness of what comes out after vulcanization. They did. And they plotted points...run charts, like this.  And I said, ‘now look, that's awful hard for me to see anything there.’ This is beginning, middle, end...beginning, middle, end..awful hard to follow.

“Let's just take the chart, plot it in a different way.  Use a dot for the beginning of the batch, an open dot for the middle. I don't care what you use. And X for the end. Plotted sixteen batches in a row.  Here they are: Sixteen in a row. one, two, three, four. Sixteen.  In every case, the end was lowest of the three, except for one tie.  Just eyeball test.  That stuff is either not mixed or it is aging.

“It's helped people. It's a simple graphical representation. Some of it's in my book, chapter thirteen. Nothing unusual. Nothing spectacular. Nothing new. Anybody can look and draw that conclusion. The stuff is aging, or it's not mixed. One or the other. They were engineers...so called. Had the privilege to study. It has helped them. Least they said it did.  Piece of paper and a pencil. Yes...

“NEW VOICE: If you had that data for sixteen in a row, where the end was always at the lower hardness, could you then do a heads and tails calculation on that?

“DR DEMING: Well hell fire, why do it?  Make a lot of nonsense out of it? Why make nonsense out of it?  There it is. We have a job to do.  Let's try to be helpful.”

The point about the p-value is well-made, too. I don’t see it as much from people claiming trends, though, as I do from people claiming significant correlations or regression models. Someone told a lot of people that a low p-value signals a significant correlation. They didn’t explain that it just signals a slope significantly different from zero. I have seen tables in peer-reviewed studies claiming significant effects from treatments with p-values of  less than .001, but r-squared values of 4.5%! The “peers” must have gone to the same stats class as the author, I guess. I try to explain that that p-value is as useful as an average phone number. 

Wouldn't using the moving Range chart (XmR) identified the two process shifts?

Rich DeRoeck