The DOE FAQ Alert Vol. 5 No. 6

Issue: Volume 5, Number 6
Date: June 2005
From: Mark J. Anderson, Stat-Ease, Inc. (http://www.statease.com)

Dear Experimenter,

Here's another set of frequently asked questions (FAQs) about doing design of experiments (DOE), plus alerts to timely information and free software updates. If you missed the previous DOE FAQ Alert, please click on the links at the bottom of this page. If you have a question that needs answering, click the Search tab and enter the key words. This finds not only answers from previous Alerts, but also other documents posted to the Stat-Ease web site.

Feel free to forward this newsletter to your colleagues. They can subscribe by going to http://www.statease.com/doealertreg.html. If this newsletter prompts you to ask your own questions about DOE, please address them via mail to:[email protected].

Here's an appetizer to get this Alert off to a good start: Maybe you should not be subscribing to this newsletter because according to an Internet posting by BBC News UK Edition, e-mail is worse than Marijuana for draining your brain (see http://news.bbc.co.uk/1/hi/uk/4471607.stm). The article reports a study showing the distraction of e-mail causing a 10-point fall in subjects' IQ—more than twice that found in studies of the impact of smoking marijuana. I'd like to think that DOE FAQ Alert, being so thought-provoking, causes a net increase in IQ. What do you think (or can you even think while reading this)?

Here's what I cover in the body text of this DOE FAQ Alert (topics that delve into statistical detail are designated "Expert"):

1. FAQ: Setting up a fractional design with multilevel factors, some of which are categoric
2. Expert-FAQ: How the prediction interval for a modeled response differs from its confidence interval
3. Info alert: Process Analytical Technology (PAT)—A framework from the US FDA encouraging DOE for pharmaceutical development
4. Book alert: There is a new edition of "Statistics for Experimenters" by Box, Hunter and Hunter
5. Events alert: Link to a schedule of appearances by Stat-Ease
6. Workshop alert: See when and where to learn about DOE

PS. Quote for the month: Uplifting advice from the author of "Silent Spring" — a landmark book on the environment.

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1. FAQ: Setting up a fractional design with multilevel factors, some of which are categoric

-----Original Question-----
From: Boston
"I am trying to help our process engineers with a DOE. They want to test four factors in the experiment—two categorical and two numeric. One of the numeric factors will be tested at three levels, and everything else is at two levels, so the total number of combinations will be 24 (3 x 2 x 2 x 2). Do you know of a good design that would allow me to meet these requirements and still be around 15 to 18 runs? I wish it was as simple as a standard 2^(4-1) half-fractional two-level factorial. The one factor (numeric) at three levels is causing the problem. Any advice?"

Answer:
Yes, the simplest approach with Design-Expert® software is to select a D-optimal design off the Factorial tab. By default it will set up a 15-run fractional design geared to fit a two-factor interaction (2FI) model with the variables treated categorically. To get a more sophisticated predictive model, right-click the two non-categoric factors and make them numeric. The program will then automatically fit the responses to a polynomial equation.

(Learn more about D-optimal factorial design by attending the three-day computer-intensive workshop "Experiment Design Made Easy." See http://www.statease.com/clas_edme.html for a course description. Link from this page to the course outline and schedule. Then, if you like, enroll online.)

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2. Expert-FAQ: How the prediction interval for a modeled response differs from its confidence interval

-----Original Question-----
From: Scotland
"I've been looking at the point prediction tool in Design-Expert software. (I think) I understand that the
standard error (SE) mean is calculated as the product of the SE-design and the standard deviation (Stdev) of the design. I am reasonably happy with what this means and how it is calculated. What I'm struggling to understand is the SEprediction. This seems to be the product of the standard deviation and the square root of one plus the standard error design squares (1+SEdesign^2). Is this correct? Where does the 1 come from in this term? I realize that what this calculation is trying to do is to take into account a variance component for the model. Why use 1 rather than the SE values for each of the components selected for the model? Any light you can shed on my confusion would be appreciated."

Answer (from Stat-Ease Consultant Pat Whitcomb):
"You've got the formulas correct. Here's why there are two of them. A regression model can be used to estimate the "true", or mean, value at a set of independent value coordinates and it can also be used to estimate a single observation at those same coordinates. Of course the estimated value of the mean and of a single observation is the same; however the errors associated with the estimates are different.

The confidence interval is expected to contain the mean, or "true," value. The prediction interval is constructed to include a single observation. It incorporates uncertainty as to the location of true value, as well as additional uncertainty associated with any single observation. The 1 added to SEdesign in the formula accounts for this extra variation.

If you want more detail, it can be found in most regression analysis text books. However, this is rarely mentioned in DOE textbooks."

Aside from the mathematical details, I would like to add that the prediction interval can be very helpful for assessing individual confirmation runs on what is hoped to be optimal conditions. Naturally results will vary. The prediction interval provides an expectation on the amount of variation.
—Mark

(Learn more about advanced tools of DOE by attending the three-day computer-intensive workshop "Response Surface Methods for Process Optimization." See http://www.statease.com/clas_rsm.html for a complete description. Link from this page to the course outline and schedule. Then, if you like, enroll online.)

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3. Info alert: Process Analytical Technology (PAT)—A framework from the US FDA encouraging DOE for pharmaceutical development

This news is bit dated, but I just became aware of it thanks to Cliff Yee, President of Northwest Analytical (NWA) in Portland, Oregon.* He said, "Good to hear your witty and interesting newsletters. How are you guys doing in response to PAT Guidelines by the FDA? I am wondering if you are seeing more investment by the Life Science industries in DOE consulting, training and software?" After tracking down the PAT Guidelines at http://www.fda.gov/cder/guidance/6419fnl.doc (Update 3/07: Link no longer available.) (also see http://www.fda.gov/cder/OPS/PAT.htm), I understand why Cliff believes it will generate interest in DOE. The document greatly encourages the use of planned statistical methods to explore how variations in component levels and process conditions will affect pharmaceuticals. If any of you readers can speak to this, please e-mail me.

*PS. NWA just announced a new version of their Quality Analyst software for statistical process control, etc. See http://www.nwasoft.com for details.

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4. Book Alert: There is a new edition of "Statistics for Experimenters" by Box, Hunter and Hunter

According to the listing at Amazon (see below), on May 27 Wiley-Interscience published "Statistics for Experimenters: Design, Innovation and Discovery" the second edition of the classic book on DOE by George E. P. Box, J. Stuart Hunter, and the late William G. Hunter. Stat-Ease has a copy on order. According to the publisher, the "Second Edition is thoroughly revised and updated to reflect the changes in techniques and technologies since the publication of the classic First Edition. Among the new topics included are:

- Graphical analysis of variance
- Computer analysis of complex designs
- Simplification by transformation
- Hands-on experimentation using response surface methods
- Further development of robust product and process design using split-plot arrangements and minimization of error transmission
- Introduction to process control, forecasting, and time series."

What intrigues me most, is the promise of "An appendix featuring quaquaversal quotes from a variety of sources ranging from noted statisticians and scientists to famous philosophers that embellish key concepts and enliven the learning process." I had to look up the word "quaquaversal." (It blew away my spell-checker!) I will not spoil your fun trying to decipher what it means.

For more details on this new edition from Box, Hunter and Hunter, click this link for the listing at Amazon: http://makeashorterlink.com/?K1F42272B.

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5. Events alert: Link to a schedule of appearances by Stat-Ease

Click on http://www.statease.com/events.html for a list of appearances by Stat-Ease professionals. We hope to see you sometime in the near future!

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6. Workshop alert: See when and where to learn about DOE

See http://www.statease.com/clas_pub.html for schedule and site information on all Stat-Ease workshops open to the public. To enroll, click the "register online" link on our web site or call Stat-Ease at 1.612.378.9449. If spots remain available, bring along several colleagues and take advantage of quantity discounts in tuition, or consider bringing in an expert from Stat-Ease to teach a private class at your site. Call us to get a quote.

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I hope you learned something from this issue. Address your general questions and comments to me at: [email protected].

Sincerely,

Mark

Mark J. Anderson, PE, CQE
Principal, Stat-Ease, Inc. (http://www.statease.com)
2021 East Hennepin Avenue, Suite 480
Minneapolis, Minnesota 55413 USA

PS. Quote for the month: Uplifting advice from the author of "Silent Spring"—a landmark book on the environment:

"Those who dwell among the beauties and mysteries of the Earth are never alone or weary of life."
—Rachel Carson (1907–1964)

(What amazes me is the multitude of eagles now seen around my home in the scenic Saint Croix valley bordering Minnesota and Wisconsin. They had disappeared entirely for decades, but thanks in large part to Carson's dire warnings about DDT and its harmful impact on eggs, the birds are back.—Mark)

Trademarks: Design-Ease, Design-Expert and Stat-Ease are registered trademarks of Stat-Ease, Inc.

Acknowledgements to contributors:
—Students of Stat-Ease training and users of Stat-Ease software
—Fellow Stat-Ease consultants Pat Whitcomb and Shari Kraber (see http://www.statease.com/consult.html for resumes)
—Statistical advisor to Stat-Ease: Dr. Gary Oehlert (http://www.statease.com/garyoehl.html)
—Stat-Ease programmers, especially Tryg Helseth (http://www.statease.com/pgmstaff.html)
—Heidi Hansel, Stat-Ease marketing director, and all the remaining staff

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Interested in previous FAQ DOE Alert e-mail newsletters?
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#1 Mar 01, #2 Apr 01, #3 May 01, #4 Jun 01, #5 Jul 01 , #6 Aug 01, #7 Sep 01, #8 Oct 01, #9 Nov 01, #10 Dec 01, #2-1 Jan 02, #2-2 Feb 02, #2-3 Mar 02, #2-4 Apr 02, #2-5 May 02, #2-6 Jun 02, #2-7 Jul 02, #2-8 Aug 02, #2-9 Sep 02, #2-10 Oct 02, #2-11 Nov 02, #2-12 Dec 02, #3-1 Jan 03, #3-2 Feb 03, #3-3 Mar 03, #3-4 Apr 03, #3-5 May 03, #3-6 Jun 03, #3-7 Jul 03, #3-8 Aug 03, #3-9 Sep 03 #3-10 Oct 03, #3-11 Nov 03, #3-12 Dec 03, #4-1 Jan 04, #4-2 Feb 04, #4-3 Mar 04, #4-4 Apr 04, #4-5 May 04, #4-6 Jun 04, #4-7 Jul 04, #4-8 Aug 04, #4-9 Sep 04, #4-10 Oct 04, #4-11 Nov 04, #4-12 Dec 04, #5-1 Jan 05, #5-2 Feb 05, #5-3 Mar 05, #5-4 Apr 05, #5-5 May 05, #5-6 June 05 (see above)

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