Issue: Volume 2, Number 11
Date: November 2002
From: Mark J. Anderson, Stat-Ease, Inc.
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, click on the links below. Feel free to forward this newsletter to your colleagues. They can subscribe by going to http://www.statease.com/doealertreg.html.
Here's something to loosen you up for the serious statistical stuff. It's about beer - a bit late for OctoberFest, but why not? Go to http://www.improbable.com/ig/ig-pastwinners.html and click on the link labeled "Demonstration of the Exponential Decay Law Using Beer Froth" to find out what University of Munich researchers say about comparative performance of Erdinger, Augustiner and Budweiser (Czech's Budvar brand, not the one brewed in USA by Busch). The authors suggest using this as a classroom demonstration. I raise my mug to that!
For another diversion from your daily grind, I offer the following heads-up on the upcoming Leonid meteor shower. On November 19th the Earth will pass through two of Comet Tempel-Tuttle's debris streams. The first encounter should cause a flurry of meteors over Europe and Africa around 0430 UT. The second encounter favors North Americans who are likely to see an outburst around 5:30 a.m. EST or 10:30 UT. (Note: UT is Universal Time, also known as Greenwich Mean Time.) For more details, see http://science.nasa.gov/headlines/y2002/10may_leonids-2002.htm and http://aio.arc.nasa.gov/~leonid/1998.html. (Update 3/07: This link has changed to http://leonids.arc.nasa.gov/.) If you've got any beer left from the froth experiment, bring it along for the meteor- watching, or better yet: schnapps, a traditional warmer-upper here in Minnesota. It's said that real German schnapps (not the imitations made in the USA) will curl your toes at a hundred paces, so it should get you seeing things (but maybe not meteors!).
Here's what I cover in the body text
of this DOE FAQ Alert (topics that delve into statistical detail are designated
1. FAQ: How to view a scatter plot of raw experimental data
2. Expert-FAQ: How to contend with covariates
3. Info Alerts:
a. A new class of designs is unveiled (see link to paper)
b. DOE for Six Sigma (see link to article)
c. Mixture design for rubber and play putty
4. Events alert: DOE overview in Orlando
5. Workshop alert: Upcoming classes (San Jose, etc.) plus comments on what Stat-Ease offers for Six Sigma Black Belts
6. Reader feedback: World's largest flying disk (see an unbelievable photo!)
PS. Quote for the month - Linus Pauling's metaphor on flying as it relates to science
1 - FAQ: How to view a scatter plot of raw experimental data
From: Many hapless experimenters :(
"Help - I can't find any effects!"
Answer (from Shari Kraber, Stat-Ease
"It may be true that no statistically significant effects can be found in your results. What you may not know is that our Design-Expert® and Design-Ease® software offer the View, Graph Columns option to display a scatter plot of your experimental data. I highly recommend the use of this visual inspection tool. In cases like your's (no significant outcome), you will see a wide scattering of response points across the plot, which provides an immediate understanding of why this disappointing outcome occurred. The next step is to check into the accuracy of your response measurements and quantify the inherent noise from your process. If these are not a big concern, the conclusion may simply be that the factors didn't impact these responses, at least not over the ranges you tested."
(Learn more about detecting effects from two-level factorial designs by attending the 3-day computer-intensive workshop "Experiment Design Made Easy." For a complete description see http://www.statease.com/clasedme.html. Link from this page to the course outline and schedule. Then, if you like, enroll online.)
2 - X-FAQ: How to contend with covariates
"I recently completed your Experiment Design Made Easy (EDME) workshop in Philly. Great course! I asked the instructor, John Guerin, how Design-Expert version 6 (DX6) software handled covariates. He gave me the instructions, but I'm not sure I'm doing it correctly. I was instructed to add the covariates after the initial design was made and after I added the response data. The problem is that DX6 still treats the (newly inserted) covariates as factors with two levels. I'm simulating an upcoming experiment where I have uncontrollable factors (covariates). I need to know if these covariates are significant or not. But, I don't want it appearing in my 2 or 3 factor interactions (graphs) as if I had control of these factors -- and appearing as if they had two levels (like the rest of the true controllable factors). The fact of the matter is that my covariates could have much more than two levels. For example, temperature of product coming from the process area could range from 100 to 110 degrees. If this covariate factor proves to be significant, it appears in the 2 or 3 factor interaction graphs as having only two levels. Is there a way you can outline in simple terms how to handle my covariates."
John was right on with his suggestion. However, as you say, it is a bit tricky to implement with DX6. It requires that you change the method of analysis from factorial to polynomial, which you can do by right-clicking the top of each response column under the Edit Info option. You then must tailor your polynomial models to deal properly with the two-level factors (control) versus the covariate(s) creating noise in your system. For example, let's say you start with a 2^3 design on your "control" factors and then add a 4th factor (D) to deal with excessive noise. The polynomial model you should fit first is:
Y = f(Mean, A, B, C, D, AB, AC, AD, BC, BD, CD, D^2)
(Note that the only squared term is on D, because presumably it's the only factor that will take on more than two levels.) Then see if you can eliminate any insignificant terms via model reduction. If interactions between control factors remain in the model, you can see them under Model Graphs by clicking the View menu and choosing Interactions.
(Learn more about developing good polynomial models by attending the "Response Surface Methods for Process Optimization" workshop. For a description, see http://www.statease.com/clas_rsm.html. Link from this page to the course outline and schedule. You can enroll on-line by linking to the Stat-Ease e-commerce page for workshops.)
3 - Info alert:
a. A new class of designs unveiled
Last month Stat-Ease statistical consultant Pat Whitcomb and our advisor, Professor Gary Oehlert, unveiled a new class of designs that offer good value for industrial experimenters who cannot afford to do more runs than necessary for adequate response modeling. Their talk, entitled "Central Composite Designs from Small, Optimal, Equireplicated, Resolution V Fractions of 2^k Designs," was presented at the Fall Technical Conference (FTC) in Valley Forge, Pennsylvania. For all the details, see http://www.statease.com/pubs/small5.pdf.
b. Six Sigma article
This e-mail arrived last month:
"Hello Mark, Congratulations! Your recent article submission ("Achieving Six Sigma Objectives for Variability Reduction in Formulation and Processing: Apply powerful design of experiments (DOE) tools to make your system more robust to variations in component levels and processing factors") has been approved by our editors. You should be proud of this accomplishment as it exceeds the quality of most submissions. Please don't hesitate to write with any questions or future content submissions. We look forward to a long relationship with you, and thank you for sharing your invaluable experience and insights with the 240,000 monthly iSixSigma readers."
See http://www.isixsigma.com/tools-templates/design-of-experiments-doe/reducing-variability-doe/ for this article, but watch for the following typo caught by an astute reader: "standard deviation is given with the term (15 - 1.4 *X1). The constant should be 25, not 15."
c. Mixture design for rubber and play putty
See http://www.statease.com/pubs/mixdoe.pdf for an article entitled "Mixture DOE Uncovers Formulations Quicker" that appeared in "Rubber & Plastics News" last month. It includes a design on play putty that will be discussed in more detail in an upcoming "Stat-Teaser" newsletter. Keep your heads up!
4 - Events alert: DOE overview in Orlando
Pat Whitcomb will present an overview on design of experiments on November 18 at the International Wire & Cable Symposium in Orlando, Florida. He will be assisted by Timothy E. Myers, R&D Technical Manager, Fiber Optic Materials, Borden Chemical Inc. See http://www.iwcs.org/# for details.
Click http://www.statease.com/events.html for a listing of where Stat-Ease consultants will be giving talks and doing DOE demos. We hope to see you sometime in the near future!
5 - Workshop alert: Upcoming classes (San Jose, etc.), plus comments on what Stat-Ease offers for Six Sigma Black Belts
See http://www.statease.com/clas_pub.html for schedule and site information on all Stat-Ease workshops open to the public. The next class will be Experiment Design Made Easy on December 10-12 in San Jose, California. To enroll in this or any other upcoming workshop, click the "register online" link at 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.
We're frequently asked whether Stat-Ease offers training for Six Sigma Black Belts. Here's a good answer from Shari Kraber, one of our statistical consultants: "Stat-Ease does not offer Six Sigma Black Belt training directly. However, we do offer a wide variety of classes on both design of experiments and general statistics. The tools that we teach are vital to the Six Sigma program, but we teach them at a more in-depth level than the typical Six Sigma training programs. Workshops can be brought on-site or you can attend our public workshops in Minneapolis. Our design of experiments classes include workshops to learn factorial designs, response surface designs, and robust design for reducing variation. We also offer the Statistics for Technical Professionals workshop where we teach how to use confidence intervals, tolerance intervals, hypothesis testing and determination of sample sizes (for more description, see http://www.statease.com/clas_stp.html.) In addition to training, we offer consulting services to help clients with the statistical aspects of their Six Sigma projects."
6 - Reader feedback: World's largest flying disk
----- Original Message -----
From: Darrell W. Pepper, Ph.D., Dean, College of Engineering, University of Nevada Las Vegas
"I enjoyed your article in the September issue of the Stat-Teaser [see http://www.statease.com/newsltr.html] regarding the flying rings/disks with your daughter. I just thought you might like to know that we built the world's largest flying disk (10 ft in diameter) some years ago - as well as a 10 ft ring (using mylar and PVC pipe). I also had a grad student do his MS thesis on frisbee/disk aerodynamics a few years back. See the attached picture [posted at http://www.statease.com/images/bigfrisbee.gif] of one of our former engineering students (who also played center for the UNLV football team) actually throwing the disk (Adler design - like Aerobie [see http://www.aerobie.com/] but solid). The disk was made from composite material and foam - total weight was about 20 lbs. The student tossed the disk about 75 feet. By the way, when we transported it to Reno for the annual AIAA meeting (about 400 mi), a wind came up and blew it off the trailer - the student walked over 1000 feet in the desert to pick it up (an unofficial distance record?) The following year I had some students work on a giant machine to toss the disk. It never materialized, but the idea seemed good. We then went on to build solar airplanes, etc. One more thing - there was a report of a UFO disk-shaped object flying over the highway."
I think the perfect college semester would be made up of two classes, one by you on aerodynamics and the other from the profs at U of Munich (see earlier note on their studies).
I hope you learned something from this issue. Address your questions and comments to me at:
Mark J. Anderson, PE, CQE
Principal, Stat-Ease, Inc. (http://www.statease.com)
Minneapolis, Minnesota USA
PS. Quote for the month -
a metaphor on flying as it relates to science: "Facts
are the air of scientists. Without them you can never fly."
- Linus Pauling
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.
Interested in previous FAQ DOE Alert e-mail newsletters? To view a past issue, choose it below.
#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 (see above)