RE: Special Causes Indicators in Red Bead

[Rip Stauffer <rstauffer@bluefirepartners.com>]

Paul Hollingworth asked: "Say we took Steven's numbered beads and then used
a random number generator to select sets of 50 beads. What effect would this
have on the red bead count and thus the control limits and mean?

"Why?"

I did this a few years ago, using two sets of one million random numbers
each, one from the RAND Million Random Numbers and one from a geiger counter
hooked up to a Krypton source to record cycle time for radioactive decay.
Random sampling produced very tight confidence intervals (within around the
population means, demonstrating the effectiveness of enumerative studies
when studying static populations. Deming pointed out on numerous occasions
that enumerative studies do work very well. When you have a frame, you have
a large body of statistical theory that works beautifully. In OOC, p 353:

"If we were to form lots by use of random numbers, then the cumulated
average, the statistical limit of [x-bar], would be 10. The reason is that
the random numbers pay no attention to color, nor to size, nor to any other
physical characteristic of beads, paddle, or employee. Statistical theory
(theory of probability) as taught in the books for the theory of sampling
and thwory of distributions applies in the use of random numbers, but not in
the experiences of life. Once statistical control is established, then a
distribution exists, and is predictable."

Earlier, on p 352, he said, "The difference between the accumulated [rbar]
and 10 is often alluded to by people in the audience as bias. No, this
difference is not bias. It is the difference between two methods of
selection:  (1) mechanical sampling, used here; (2) selection by random
numbers."

I compared my results to averages from 5000 paddles, 2500 each from two
different red bead setups (one plastic with plastic paddle, one wooden with
steel paddle). One had an xbar (npbar) close to 9, the other close to 10.5.
This set of experiments demonstrated and supported Dr. Deming's assertions,
and those of many others. (Not that I ever thought it wouldn't, but I was
used to dealing with skeptics and I thought maybe this amount of evidence
might help sway some of the unconvinced).

I further suggested (and this kicked off some lively debate during a
presentation at the Spring Conference a couple years ago) that this not only
demonstrates the difference between mechanical and random sampling, but also
provides an excellent analog for comparing analytic and enumerative studies.
I wish I could take credit for that idea, but David Kerridge had postulated
it earlier in the DEN. 

I believe that mechanical sampling is a process, and that the Red Bead is an
idealized production process. When we assign each of the beads a number and
draw them via a random number table, we are using the beads as a population
and enumerating the frame. When we mix them and draw them using a paddle, we
are following a process ("our process is absolutely rigid!"). The context is
not static anymore; the "population" no longer exists in a very real sense.
We have turned the bowl into a "bottomless" bowl, and could be drawing from
a stream of beads coming off a production line. By placing the number of
"defectives" on a contol chart, we are using the results of the past to
predict within limits the results for the future. The control chart
characterizes the mechanical sampling process I am using.

This difference is little understood, outside of this circle. There are a
number of people still trying to do hypothesis tests on process data,
whether the processes exhibit statistical control or not. The difference
between sampling and subgrouping is not well understood. The techniques that
are appropriate for enumerative studies are probably not appropriate for
answering the questions and guiding the actions for which you would do an
analytic study. In TNE, Dr. Deming points out: "Use of data requires also
understanding of the distinction between analytic and enumerative studies.
An enumerative study produces information about the frame. The theory of
sampling and design of experiments are enumerative studies.... The
interpretation of results of a test or experiment is something else. It is a
prediction that a specific change in a process or procedure will be a wise
choice, or that no change would be better. This is known as an analytic
problem, or a problem of inference, prediction. Tests of significance,
t-test, chi-square, are useless as inference--i.e., useless for aid in
prediction. Test of hypothesis has been for half a century a bristling
obstruction to understanding statistical significance.

There is some recent light. Bill Woodall's presentation last year at the
ASA/ASQ Statistical Division Fall Technical Conference (the paper is in the
October 2000 issue of the Journal of Quality Technology) brought some of the
issues to the fore; there seems to be a lot of support for Shewhart's
assertion that we can't assume any distribution in a data from a process
without evidence of statistical control. There are certainly cases where
characterising some product through random sampling (as in the wool blanket
example) might produce data that might then be used to characterise the
producing process over time. There are also cases where one might want to
compare the product from two "stable" production lines. This could be done
on control charts, of course; one point the discussants made is that if the
data come from "stable" processes they could be treated as though they are
populations and compared using hypothesis 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
mailto:rstauffer@bluefirepartners.com
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