Issue: Volume 4, Number 2
Date: February 2004
From: Mark J. Anderson, Stat-Ease, Inc. (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 previous DOE FAQ Alerts, please click on the links at the bottom of this page. 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 ask to your own questions about DOE, please address them to stathelp@statease.com.

Here's food-for-thought to get this Alert off to a good start. Does an Internet-based poll prove that seven is the least random number? See http://www.macpolls.com/?poll_id=332 for the results based on over 4000 responses.  Consider this the next time someone says they've thought of a number and you, along with several other contestants, are provided with the opportunity to match it for some sort of favor.  Seven might be a good choice!

Now for some sleep-for-thought: Researchers from University of Lubeck in Germany reported recently in Nature magazine that sleep may help people solve math problems.  See the news on this at http://www.mercurynews.com/mld/mercurynews/news/7769015.htm. (Update--3/07: This link is no longer active.) Note the cautionary comments from Dr. Dement.  Despite the odd name, this fellow provides good advice on waiting for confirmation before ramping up your sleep in hopes of getting smarter. However, it certainly seems worth the try!

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: Interpreting the standard error plot  
2. FAQ: Do a factorial design with center points or use response surface methods (RSM)?  
3. Info alert: Get your successful study into print (a link is provided to an inspirational article)  
4. Events alert: Link to a schedule of appearances by Stat-Ease, including Six Sigma training at the Ohio State University  
5. Workshop alert: See when and where to learn about DOE -- A class is coming to Philadelphia

PS. Quote for the month -- Why Apple has not lived up to its technical promise: Voltaire provides the answer.  (See the link to an article on Steve Jobs and the limits of innovation.)

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1. FAQ: Interpreting the standard error plot

-----Original Question-----
From: "iSixSigma Discussions," January 22, 2004, Vol. 5, #6
Via: A tip from a regular correspondent -- "Mark, there's a question about standard error with reference to Design-Expert in this newsletter.  I thought you might want to be aware of it, possibly respond to it, or include a note about the topic in your newsletter."  Signed: "Your friendly, neighborhood statistician" Arved Harding

Here is the actual question posted at http://www.isixsigma.com/forum/showmessage.asp?messageID=38517:
"I'm trying to understand the meaning of the Std Err in the DOE.  Design-Expert provides a good visualization of the standard error over the design space depending on the type of design selected.  I've understood that this parameter represents the goodness of the prediction but I don't understand the exact meaning.  What exactly is this number?  How can I use it?  Looking at its value in a point of the design space can I determine the uncertainty of my prediction?

Can anybody help me or indicate a good reference on this topic?"

Answer (from Stat-Ease consultant Pat Whitcomb):
"Design-Expert software reports the standard error (SE) of the predicted mean.  The larger the standard error, the less reliable the estimate.

Prior to running the design the actual process variation is not known so the program plugs in a value of one for the standard deviation (sigma) so it can generate the SE plot (done via Design Evaluation -- Graphs).  The shape depends only on the runs in the planned design and the polynomial being fit.  After the design is completed the estimated sigma becomes a multiplier for the value of one assumed beforehand. Therefore the magnitude of the standard error is changed but not the appearance of the SE plot.

In any case (before or after doing the DOE -- it does not matter), the design ideally produces a flat error profile (an area of uniform precision) centered in the middle of your design space.  For a response surface method (RSM) this should appear as either a circle or a square -- preferably exhibiting symmetry."

Professor Gary Oehlert of the University of Minnesota School of Statistics, who advises Stat-Ease, adds this qualifier: "This standard error is a good statement of reliability only if the model that we are fitting is a good match for the true, but unknown, response surface.  If the true surface has features that our model cannot reproduce (for example, discontinuities), then there will be systematic error in addition to the stochastic error reported in the SE."

Click http://www.statease.com/x6ug/DX06-RSM.pdf and select page 23 to see a 3D view of standard error from a rotatable central composite design (CCD).  The flat-bottomed bowl shape is very desirable.  In this case the shape is spherical.  However, as Myers and Montgomery (M&M) point out, it would not be bad if a design produces a cuboidal SE plot, such as that seen from a face-centered central composite design (FCD).  Here's a quote from M&M's textbook, "Response Surface Methodology"* (page 335): "[When] the region of interest and ... operability are the same,...the obvious region for the design is a cube." M&M define the SE of predicted response on page 262 of their book. They show many SE plots from Design-Expert further on, particularly in section 7.4 -- "Designs for Fitting Second-Order Models."
*(2nd Ed., Wiley, 2002, available via Stat-Ease e-commerce site at http://www.statease.com/prodbook.html.)

(Learn more about standard error 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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2. FAQ: Do a factorial design with center points or use response surface methods (RSM)?

-----Original Question-----
From: Certified 6s Black Belt, New York

"I have an experiment to do on 3 factors. I want three levels for each factor.  I am quite sure that quadratic terms will be insignificant.  What is the best possible design:  
1. 2^3 = 8 runs with a few replications at the center point  
2. 3^3 = 27 runs with a few replications at the center point  
3. Face-centered central composite design = 15 runs + a few runs at the center?"

"I have an engineer who performed as a two-level factorial experiment.  I've told him to analyze the experiment using ANOVA, but he says he usually does a two-sample t-test and then only if he finds anything suspicious does he bother doing an analysis of variance.  He claims that it's OK to 'project' the factorial experiment into one factor and then only the t-test will be needed.  Is my engineer correct in simplifying things this way?"

Answer:
Your first option is best, but do at least 4 replications of the center point for decent power on the curvature test.  If curvature comes out significant, then augment the design with a second block of runs to make it into either a central composite design (CCD) or a face-centered composite design (FCD), depending on whether you can go outside the original factorial ranges.  Design-Expert offers this feature under its "Design Tools" option. Select "Augment Design" and go with the default choice to create a Central Composite design (CCD). The software then adds the runs needed to apply response surface methods (RSM). After performing these runs and entering the resulting responses, you then can get a better picture of how your response depends on the input factors.

(Learn more about center points, and what to do if they reveal curvature, by attending the three-day computer-intensive workshop "Experiment Design Made Easy."  For a course description, see http://www.statease.com/clas_edme.html.  Link from this page to the course outline and schedule. Then, if you like, enroll online.)

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3.  Info alert: Get your successful study into print (a link is provided to an inspirational article)

Former Stat-Ease Marketing Director, Richard Burnham, wrote an inspirational article for technical professionals who want to publicize their successful studies.  "The Business to Business Marketer" (B2B) picked it up for their cover feature.  Check it out at http://www.statease.com/pubs/eng-marketers.pdf.  Rich's article is titled "Engineers as Credible Marketers."  He now works independently as a technical writer (see his web site at http://www.PublicationCoordination.com/) including projects sponsored by Stat-Ease.  We offer technical writing services to any Stat-Ease client who wishes to get their DOE into print as a case-study article in their favorite trade publication.  The article by Rich explains what's in it for you.  He's been instrumental in getting to print many of the case studies we've posted at http://www.statease.com/articles.html.

If you have a success story to tell about an experiment done via statistical design (preferably facilitated by Stat-Ease software and/or training), please e-mail our Marketing Director, Heidi Hansel, at Mailto:[email protected].

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4. Events alert: Link to schedule of appearances by Stat-Ease, including Six Sigma training at the Ohio State University

Ann Ramsey, Program Manager of Fisher College of Business Executive Education at the Ohio State University (OSU) passes along the following details about their "web-leveraged" education on Six Sigma:

"If you're in a competitive industry where there is less and less room for error; if quality is key and old business models no longer work, then you should become more familiar with one of the most widely discussed and reported business trends: Six Sigma.  Fisher College of Business at The Ohio State University and MoreSteam.com have teamed up to bring you a premier Six Sigma training program featuring the best combination of online and in-class sessions, presented by top instructors and practitioners.  Featuring only one full week of in-class experience and a world-class online program, this training is the most time-sensitive, value-driven program in existence today."

To see a brochure (note that I am listed on the faculty), click on http://fisher.osu.edu/exec/operations/sixsigma/sixsigma.pdf. Also see http://fisher.osu.edu/exec/operations/sixsigma/index.htm.
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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5. Workshop alert: See when and where to learn about DOE -- A class is coming to Philadelphia

"Experiment Design Made Easy" (EDME) will be coming to Philadelphia March 30 through April 1 (no fooling!).  However, if you cannot wait until then, or find Minnesota more convenient, we welcome you to the Stat-Ease training center for an earlier EDME: February 24-26, (Minneapolis).

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 on 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: mark@statease.com

Sincerely,

Mark

Mark J. Anderson, PE, CQE
Principal, Stat-Ease, Inc. (http://www.statease.com)
Minneapolis, Minnesota USA

PS. Quote for the month -- Why Apple has not lived up to its technical promise—
Voltaire provides the answer:

"The perfect is the enemy of the good."

-- Voltaire (1694 - 1778) (See this quote and general theme in an article by "Fast Company" published in their January issue titled, "If He's So Smart...Steve Jobs, Apple, and the Limits of Innovation."  It is posted at http://www.fastcompany.com/magazine/78/jobs.html.)

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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#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 (see above)

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