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Issue:
Volume 7, Number 2
Date:
February 2007
From:
Mark J. Anderson, Stat-Ease, Inc., Statistics Made Easy® Blog
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].
For an assortment of appetizers to get this Alert off to a good start, see these new blogs at http://statsmadeeasy.net:
— "Nature's dangerous forces — including cold temperatures"
— "Making coffee to the most by taking on the roast" (also see the comment)
— "Quest against greenhouse gases takes on religious fervor" (and comment)
— "Mixing beers — synergy of zymurgy?"
Topics in the body text of this DOE FAQ Alert are headlined below (the "Expert" ones, if any, delve into statistical details).
1. FAQ: Does it make sense to add center points in a screening design that may lack power?
2. Expert-FAQ: Cox versus Piepel trace plots for analysis of mixture experiments
3. Reader Response: More reaction to Jeff Hybarger's popular article "The Ten Most Common Designed Experiment Mistakes"
4. Events Alert: Do you seek a speaker on DOE?
5. Workshop alert: Mixture design workshop coming to San Jose
PS. Quote for the month: How "Freakonomics" derives its controversial conclusions. (Page through to the end of this e-mail to enjoy the actual quote.)
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1. FAQ: Does it make sense to add center points in a screening design that may lack power?
-----Original Question-----
From: Tennesee
"I'm planning to use a minimum-run resolution IV design (MR4*) design for to screen 9 factors for the vital few. I will use your program default of adding 2 extra runs — just in case of a few problems during the course of experimentation. Given my needs to detect a signal of 1.5 standard deviations, your software reports power a bit above 80 percent on all main effects. Do you advise I add center points to increase the power?"
Answer:
Center points (CPs) do not help much for power and, furthermore, they are not needed for screening — add them as a check for curvature in your next phase of process development — the followup experiment on the surviving factors. In your case, adding 4 CPs to a 20-run MR4+2 increases power only two percent.
If power proved to be more problematic, for example — on another response that required detection at 1 standard deviation, you would do much better by going back to the standard catalog of two-level factorials and choosing the 32-run eighth-fraction (2^9-4) with no CPs. In this case, the power increases to near
the ideal minimum of 80 percent, whereas the MR4 of 20 runs produces less than 50 percent power. I commend you for realizing that power should be assessed in the design phase* — not after completing what may prove to be a weak experiment. However, center points are more of a luxury than a necessity for screening purposes.
(Learn more about power in factorial design by attending the three-day computer-intensive workshop "Experiment Design Made Easy." See http://www.statease.com/clas_edme.html for a description of this class and then link from this page to the course outline and schedule. Then, if you like, enroll online.)
*MR4 and MR5 designs come with version 7 of Design-Ease® and Design-Expert® software. See program overviews at http://www.statease.com/soft_abs.html and link from there to details and free 45-day fully-functional trials.
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2. Expert FAQ: Cox versus Piepel trace plots for analysis of mixture experiments
-----Original Question-----
From:Rochester, New York
"Can you explain the difference and provide some guidelines on Cox versus Piepel trace plots: Which one should I use?"
Answer:
See graphic details on how Cox and Piepel vary in their trace plot direction at http://www.statease.com/pubs/cox-vs-piepel.pdf. The following paragraphs provide further background and explanation.
In the early 1970's Cox developed a trace plot that shows the effects of changing each mixture component while holding all others in a constant ratio. The response is plotted while moving along an imaginary line from a reference blend to the vertex of the component being incremented. The default reference blend is the centroid of the design. As the amount of this component increases, the amounts of all other components decrease, but their ratio to one another remains constant. For example, in a three-component simplex design, a response trace can be generated as A increases along the line from the overall centroid (A=1/3, B=1/3, C=1/3) toward its pure component vertex (1,0,0). In this case, as the amount of A increases, the amounts of B and C decrease, but the ratio of B to C stays constant at a one-to-one ratio.
In his detailing of Cox's innovation, Cornell* passes along this enlightening analogy by Lynne Hare (page 255): "It is easy to visualize an experimenter pouring ingredient 'i' into a beaker and getting a continuous reading of the response." A decade after Cox's innovation, Piepel introduced a refinement to trace plots when the mixture region is constrained. It works on the basis of pseudocomponents. In Piepel’s direction the ratios of the 'changeable' amounts of all the other components are held constant. On either the Cox or Piepel trace plot, a steep slope or curvature in an input variable indicates a relatively high sensitivity of response. These influential components are good ones to select for the axes on the 2D and 3D contour plots. If the response fits a linear model, you may not need the more sophisticated response plots, because the trace plot tells the story. For example, see the case study on producing a better pound cake detailed at http://www.stat-ease.com/pubs/cake.pdf. As a chemical engineer, I prefer Cox for maintaining constant ratios (stoichiometry). However, when plotted in this direction, traces for highly-constrained mixture components, such as a catalyst for a chemical reaction, become truncated. Thus, experts in mixture design like my colleague Pat Whitcomb, argue that, although it no longer holds actual ratios constant, Piepel's direction provides a more helpful plot by providing the broadest coverage of the experimental space. For this reason Piepel is the preferred plot in our Design-Expert (DX) software. In general, trace plots are highly dependent not only on direction (Cox vs Piepel for example), but also on where you place the starting point (by default, the centroid). Consider that the traces are one-dimensional only, and thus cannot provide a very useful view of a response surface. The 3D response plots provide better pictures of the surface and ultimately provide the basis for numerical optimization — the ultimate tool for determining the most desirable mixture composition. In the end it may make no difference as a practical matter which plot you use. If that is the case, all worries about Cox versus Piepel are over! Unfortunately for your particular data, tracing the predicted response via Cox versus Piepel makes some components look quite different in their impact. That tells me that you really ought to use the 2D contour and 3D surface plots to draw inferences — not the 1D trace.
(Learn more about mixture design by attending the three-day computer-intensive workshop "Mixture Design for Optimal Formulations." For a complete description of this class, see http://www.statease.com/clas_mix.html. Link from this page to the course outline and schedule. Then, if you like, enroll online.)
*("Experiments with Mixtures: Designs, Models, and the Analysis of Mixture Data," 3rd Edition — available for purchase at http://www.statease.com/prodbook.html.)
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3. Reader response: More reaction to Jeff Hybarger's popular article "The Ten Most Common Designed Experiment Mistakes"*
-----Original Response-----
From: Christopher T. Nance, Courtney Group Resources ASQ Certified Six Sigma Black Belt, Certified Quality Engineer "I think the most common mistake in experimental design is inadequate ranges set for the factors, which will often cause a factor to appear insignificant when it actually is significant. I fought this battle for years at my former employer, where people thought they were being more precise by having a small amount of variation in the factors."
-----Original Response-----
From: James M. Malone, III
"With so much theory...there is the danger of focusing on that in detail and not placing it in the context of applications. ...
Applied statistics relies heavily on "heuristics" — which may be exploited in the great majority of situations. An urgent need is an explicit listing of such heuristics with an evaluation of their usefulness."
*[http://www.statease.com/news/news0612.pdf]
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4. Events alert: Talk for Lafayette, Indiana ASQ Section.
See the Stat-Ease display at the Biomedical Focus Conference, Monday, February 12 in Brooklyn Center, Minnesota. Details are provided at http://008722b.netsolhost.com/content.aspx?pid=12 .
The evening of Tuesday the 13th I will present a talk to the Lafayette Indiana section of ASQ (American Society of Quality), which includes an active group of students from Purdue U.
Click 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!
PS. Do you need a speaker on DOE for a learning session within your company or technical society at regional, national, or even international levels? If so, contact me. It may not cost you anything if Stat-Ease has a consultant close by. However, for presentations involving travel, we appreciate reimbursements for airfare, hotel and meals — expenses only. In any case, it never hurts to ask Stat-Ease for a speaker on this topic — we are at the foremost ranks of practical expertise on design of experiments for process and product improvement. Contact me at [email protected] if you have an event coming up with an
open slot for a presentation.
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5. Workshop alert: Mixture design workshop coming to San Jose
The three-day computer-intensive workshop on Mixture Design for Optimal Formulations makes a rare appearance in San Jose, California on April 17-19. For more detail, see http://www.statease.com/clas_mix.html and link from there to the course outline and schedule. Then, if you like, enroll online. 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 class at your site.*
*Once you achieve a critical mass of about 6 students, it becomes very economical to sponsor a private workshop, which is most convenient and effective for your staff. For a quote, call and ask for Workshop Coordinator Sherry Klick.
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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 — How "Freakonomics" derives its controversial conclusions:
"Regression analysis is the tool that enables an economist to sort out...huge piles of data. It does so by artificially holding constant every variable except the two he wishes to focus on, and then showing how these two co-vary. In a perfect world, an economist could run a controlled experiment just like a physicist...but...rarely has the luxury..."
—Steven D. Levitt and Stephen J. Dubner (Page 162). See http://www.freakonomics.com/thebook.php for information about their book. I did not think much of its over-simplifications, but at least the reading was quick and thoughts were provoked. If you enjoy debate, see this reaction by 'econoblogger' Michael Stastny to the Wall Street Journal critique of one Freakonomics finding: http://mahalanobis.twoday.net/stories/1203397/. - 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
—Stat-Ease consultants Pat Whitcomb, Shari Kraber and Wayne Adams
(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 and Neal Vaughn
(http://www.statease.com/pgmstaff.html)
—Heidi Hansel, Stat-Ease marketing director, and all the remaining
staff
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