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Most of you have seen or at least heard of the article on the future of Response Surface methodology by Ray Myers in the January issue of the Journal of Quality Technology. In our lead article this month, Dr. Selden Crary presents another perspective. We are compelled by Dr. Crary's arguments, and hope that you will find them at least thought provoking.
In addition, you will find we have been busy on a number of fronts, collecting information from various sources, delivering classes, etc. This makes for a longer than usual issue, but we hope that you will find it all useful and informative.
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This article is dedicated to the memory of David Doehlert (1929-1999).
I wish to thank Al Corwin for the opportunity to address some of the issues raised in Ray Myers’ talk in Corning, New York last October [published as Raymond H. Myers, "Response Surface Methodology – Current Status and Future Directions," Journal of Quality Technology 31, pp. 30-44 (1999)]. I invite readers of DOE Perspectives to read Prof. Myers’ article, with special emphasis on the first five sections, namely: Introduction; What is RSM? What has Changed; Taguchi’s Parameter Design; Computer Generated Design – A Vast Wasteland???; and Robust Experimental Designs. Whether or not you have access to the article, read on to hear a different perspective from one who strongly advocates computational optimal design methodology in practice.
What Myers said
In the section "What is RSM? What has Changed," Myers lays out his view of the goals of response-surface methodology (RSM):
"The goals of RSM for the practitioner remains (sic) the same as described in the seminal paper by Box and Wilson. Namely, one is interested in designing an experiment on a set of quantitative process factors (or mixture of quantitative and qualitative factors) and analyzing the resulting data with the goal of determining conditions on the design variables that provide process improvement or perhaps even process optimization."
Later in the same section, he writes the following concerning future DOE challenges:
"To point to examples, we have multiple responses, more complicated models, and some scenarios unsuitable for polynomial approximations. We have incredibly large numbers of design variables and clearly nonnormal responses that question the suitability of classical designs."
In the next section, he points to the virtues of variance modeling, that is, the value of including in the objective of a designed experiment the goal of modeling the variance of the response function, in addition to the response function itself. Then in the section "Computer Generated Design – A Vast Wasteland???" Myers emphasizes two points:
"Much has been written about the utility and/or overuse of computer generated design in RSM. There is no intention here to give a complete bibliography. Different opinions reside, but two things are certain. The first is that in the past too many users have relied on design optimality when the use of standard designs, such as central composite designs (ccd’s) or Box-Behnken designs would be preferable. …The second is that if, historically, computer software companies had embraced design robustness more vigorously than design optimality, then more flexible tools would be available for use in RSM problems."
He then emphasizes the uncertainties of "choice of model, realism regarding assumptions, and even handling multiple goals in the experiment," and he concludes the section by asserting that "in many RSM situations, standard designs are more attractive because they appeal to the notions of design robustness …"
Finally, in the section on "Robust Experimental Design," Prof. Myers criticizes alphabetic optimality for its inability to handle non-linear models, calling instead for Bayesian and sequential approaches.
My view
While I think that Prof. Myers made many good points in his paper, I think he makes some critical mistakes.
First, I would add that there are other important goals in RSM than just the one he gave, such as developing a parsimonious surrogate function ("metamodel") or developing an understanding of the response function across a range of the factor space. Both of these additional objectives require a design that can give good predictive capability.
More importantly, however, I think that he greatly underappreciates the value of optimal designs and is far too sanguine about the value of standard designs. For example, let us compare the predictive capability of a rotatable central-composite design in six factors against the I-optimal design with the same number of points, for the case of a full-second-degree model function. If we consider the ccd to have 26 vertex points, 2× 6 star points, and one center point, for a total of 81 points, then it turns out that the comparable I-optimal design has a full factor of ten lower average variance of prediction over the six-dimension hypercube. This gain is not just anecdotal, but grows rapidly with the number of factors. Now the I-optimal design may not be as well balanced as the ccd, but for a factor of ten improvement in variance, I think most users would be happy to give up some balance. Another way of looking at this is that with an I-optimal design, one needs many fewer points to get the same predictive capability. Instead of 81 points, one could use the minimum number for the model function plus a few more for good measure, say 28 + 3 = 31 points.
I would add that there is nothing, in principle, that prevents optimal design software from tackling Bayesian or sequential problems. In fact, I-OPTä , a program that has been available on a University of Michigan anonymous ftp site since 1991, allows for both Bayesian and sequential approaches. There are examples, along with downloading instruction, in the I-OPT manual that is available at the following URL: http://www-personal.engin.umich.edu/~crary/iopt .
Also, there are optimal designs that can treat multiple model functions, as does I-OPT, which allows a user to enter up to ten potential model functions, along with an estimate of the likelihood that each is the correct model. Beyond this, there are even design approaches that do not require that a model be specified at all, such as the IMSE criterion given in J. Sacks et al., Technometrics, 31, pp. 41-47 (1989), which was recently updated, along with publicly available software, (see S. B. Crary et al., Proc. of the Second Int’l Conf. on Modeling and Simulation of Microsystems (MSM 99), San Juan, PR, 19-21 April 1999, pp. 184-189.
What remains is for the software community to have the vision and commitment to produce optimal design tools that address the critical issues that users require: easy access, minimal training, ease of interpretation, and flexibility to handle a wide range of linear and non-linear problems.
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If you would like to contact Dr. Crary directly, please write to him at:
Selden B. Crary, Ph.D.
University of Michigan
1301 Beal Avenue
Ann Arbor, MI 48109-2122
crary@umich.edu
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May 12-15 Atlanta, GA
The 6th Annual SIAM (Society for Industrial and Applied Mathematics) Conference on Optimization is part of this event this year. For full details, visit the SIAM web site at:
http://www.siam.org/meetings/op99/
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A Statistics Conference for Mathematics Teachers Teaching Introductory Statistics
August 5 & 6, 1999
Monroe Community College, Rochester, New York
This year's focus:
"How modern technology is effecting the teaching and learning of statistics, and how this technology can best be incorporated into the classroom."
The agenda will include:
Speakers include:
Registration Fee: $125 which includes 5 meals for participant
For complete information and updates, see our web site: http://www.monroecc.edu/depts/math/beyond1.htm
or contact Bob Johnson by:E-mail
RJohnson@MonroeCC.edu
Phone: Dept. Office: 716-292-2930
Fax: Dept. Office: 716-292-3874
Post: Dept. of Mathematics
Monroe Community College
Rochester, NY 14623
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May 17 - 19, 1999 32nd Middle Atlantic Regional Meeting; Fairleigh Dickinson University, Madison, New Jersey
June 20 - 23, 1999 54th Northwest Regional MeetingDoubletree Hotel, Columbia River; Portland, Oregon
Complete details on ACS Regional Meetings can be found at
http://www.acs.org/meetings/name.html
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Time is running out to sign up for the advanced class in Anacortes May 17th and 18th or for Ron Schoenberg's Gauss class in DC. There is little more time before the Modern DOE Workshop in Amherst, MA the week of May 26th (after Memorial Day). Please get your registrations in now if you would like to attend any of these classes.
Complete Information on all Process Builder sponsored classed can be found at:
<
http://www.processbuilder.com/doe/Classes/default.htm>
May 17, 18 -- Anacortes, WA
Bill Kappele
Advanced DOE Workshop
May 19, 20, 21 -- Washington, DC
Gauss Training Series
Ron Schoenberg
http://www.aptech.com/trng.html
Week of May 24-- Amherst, MA
Bill Kappele
A Modern DOE Workshop
Week of June 14-- Anacortes, WA
Bill Kappele
Instructor Boot Camp
Week of June 28 -- Boulder, CO
Bill Kappele
A Modern DOE Workshop
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It's been an exciting time around here with lots going on. We have received lots on input on the web site, and we hope our recent work reflects this.
In particular, check out our updated DOE links pages and our FAQ pages. This is where the bulk of the effort has been concentrated.
http://www.processbuilder.com/doe/FAQ/i-optimalit.htm
http://www.processbuilder.com/doe/Links/miscellaneous.htm
http://www.processbuilder.com/doe/Classes/performi.htm
All of the back issues are now available on-line. Pointers to these can be found at:
http://www.processbuilder.com/doe/Newsletters/BackIssues/Default.htm
If your browser cannot handle frames or the site responds too slowly over your connection, write to me and I can send you text versions of any of the following articles.
Factorial Designs and
their Flexibility
Comparing Coefficients
is Oversimplification
Run a Few; Predict the
Rest
Model Flexibility Comes
from Adding Terms
Models that are More
Flexible than Quadratic
Multiple Responses are
Common
A Personal Story of DOE
How Many Runs for How Many
Factors?
Many of Dave Doehlert's old papers and ads have been resurrected and placed on line. Many are as timely today as they were when they were written.
< http://www.processbuilder.com/doe/Dave_Doehlert/Memorabilia/Default.htm>
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We are changing the STRATEGY Pricing Policy effective immediately. Major change: STRATEGY is now free for all non-profit purposes. Please visit the following URL for full details.
< http://www.processbuilder.com/doe/Software/strategy/pricing.htm>
We are sorry to have been so slow with the maintenance upgrades. Changes to operating system level components have proven far more complex to deal with than anticipated.
A new upgrade has been completed and tested. We are building and testing the setup kits right now. Barring unforeseen problems, this setup kit will be available for download no later than May 10th.
STRATEGY 2000 is looking more and more like it will be an Internet program. We would love to get your input on this.
Thanks for your attention.
Sincerely yours,
Al Corwin
President
Process Builder