Trends up or down in Shewhart charts

[Rip Stauffer <rstauffer@bluefirepartners.com>]

Grant Blair wrote:

"1. Common cause variation is unpredictable. It behaves the same as
Shewhart's
    Bowl
2. Special Cause is predictable, even within control limits. This is why 
trend rules 
    work.
3. Special Cause is also a signal something is going on. We can PREDICT,
with
    high certainty, a search will find the condition. (or adjust, worst
    case when you see 20 is to subtract 8, then see what happens)"

This is an interesting twist, and serves as a wonderful illustration of the
idea that you must establish operational definitions before discussing
concepts. I have often been guilty of saying "common cause variation is
predictable" when what I really meant was "the LIMITS of common cause
variation are predictable." I'm still not sure I would agree completely with
Grant's point two, though. I think that once the reason for the special
cause signal is determined, you could predict the next occurrence, maybe
(hopefully you would take action to prevent the next occurrence).

Of some interest on this point, last week I attended the ASA/ASQ Stat
Division Fall Technical Conference. One session that packed the house was on
"Controversies in Statistical Process Control," a discussion of some of the
papers and topics in the upcoming JQT (Tom Ryan has mentioned this issue a
couple of times recently). 

It was a great discussion, led by William Woodall, who discussed the general
topic. The discussants were Don Wheeler and Roger Hoerl. A number of
excellent and widely-published practitioners were in the audience (Douglas
Montgomery and Alson Look, for instance). It was very encouraging to me to
see that a movement to bring researchers and practitioners together to form
a coherent system for statistical development, education and use.

OK, enough segue. Why bring this up in this discussion? One of Nelson's 1985
rules, often cited in textbooks and used in Minitab and other software, is a
trend of x points increasing or decreasing. Wheeler has discounted this rule
for years (see "Advanced Topics in Statistical Process Control," pp
136-137). What I found interestingly was that others apparently have, as
well. William Woodall mentioned this: "We have known for a long time that
these are not valid rules in control charting." I looked around, and many
were nodding; there didn't seem to be any disagreement (Note that I am NOT
claiming that there was no disagreement).

I'm not sure what all the arguments are; I am familiar with Wheeler's. As I
understand it, it's not that they don't indicate anything, they do...it's
just that other rules (runs above or below, 2 of 3 outside 2 sigma, 4 of 5
outside 1 sigma) will find special cause before it can become a progressive
trend. The runs-up-or-down rule will significantly increase the false alarm
rate. It usually involves highly autocorrelated data, and autocorrelation is
usually "self-evident without runs-up-or-down tests."

Best regards to all,

Rip

Rip Stauffer, Senior Consultant
BlueFire Partners
1300 Fifth St. Towers, 150 So. Fifth St.
Minneapolis, MN 55402
612-344-1027
rstauffer@bluefirepartners.com