Issue: Volume 3, Number 1
Date: January 2003 (Happy New Year!)
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 some appetizers to get this Alert off to a good start.
First of all, with all the unrest throughout the world as we begin the new year, it may help to get a different perspective of earth, from on high, by clicking http://makeashorterlink.com/?D323222E2. It may take a moment or two to load up, but if all goes well you will see stunning footage by the new "RocketCam" attached to one of the recent space shuttle launches. Enjoy the view and hope for peace throughout our home planet.
Now to go from the sublime to the ridiculous, see http://news.nationalgeographic.com/news/2002/12/1204_021204_Shoelaces.html for the latest technology on how to tie shoes according to mathematician Burkard Polster of Monash University in Victoria, Australia. The details on lacing most efficiently may be purely academic, but if you pursue the links on how to tie better knots, you may find something useful. Shoes now-a-days usually come with stylish round laces made from synthetic material. They may look fashionable but they come undone easily. If you are not good with knots, I suggest another solution to this problem: Try the old-fashioned flat, cotton laces. One of these days I hope to do a proper factorial design of experiments on this topic, but I must work up a lot of energy, because it will involve a lot of walking and possibly quite a few trips!
Here's what I cover in the body text
of this DOE FAQ Alert (topics that delve into statistical detail are designated
1. Software alert: A free update is available for V6.08 of Design-Expert(R) or Design-Ease(R) software (if you are not currently a user, get the free 30-day trial version)
2. Stat-Teaser alert: Preview our upcoming newsletter featuring a mixture design of experiments on play putty and the announcement of a new web-based course called "PreDOE"
3. Expert-FAQ: Problems with propagation of error (POE) not being graphed
4. Expert-FAQ: More questions about POE - specifically for mixtures, but also in general on the impact of variations in input components/factors
5. Events alert: Aerospace Sciences Meeting in Reno and other places you will find Stat-Ease
6. Workshop alert: Upcoming classes
PS. Quote for the month - New Year's resolutions from a holy man
1 - Software Alert: Free update available for V6.08 of Design-Expert or Design-Ease software (if not currently a user, get the free 30-day trial version)
If you (as an individual user) own a permanently licensed copy of version 6 of Design-Ease (DE6) or Design-Expert (DX6), go to http://www.statease.com/soft_ftp.html#dx6updt for downloads that will patch your software with the latest enhancements. We recommend you do this even though the changes may affect only a few users. To see what got added or fixed, click the "Read Me" link for either DE or DX (whichever program you will be updating).
If you own networked software that needs updating, you must call Stat-Ease customer service at 1.612.378.9449. We do not post patches for networked software on the Web. Be prepared to provide your serial number. We will then send you a replacement CD-ROM to re-install on your network.
Before updating or buying version
6 of Design-Expert, feel free to download a fully-functional, but 30-day limited,
version of the software from http://www.statease.com/dx6trial.html
. Users of Design-Ease or earlier versions of Design-Expert (V5 or before) should
consider upgrading their software to DX6. See why you should do it at http://www.statease.com/dx6descr.html
. Then call Stat-Ease for a quote. After validating your current serial number,
we will give you a special upgrade price.
2 - Stat-Teaser alert: Preview
our upcoming newsletter featuring a mixture design of experiments on play putty
and the announcement of a new web-based course called "PreDOE"
We just mailed many of you a printed copy of the latest Stat-Teaser, so this may be a 'sneak preview.' Others, particularly those who reside outside of North America, receive only the electronic copy, which can now be viewed at http://www.statease.com/news/news0212.pdf .
The feature article, "Play Putty Makes Mixture Design Simple and Fun," describes how I made use of mixture design to optimize properties of play putty. This stuff may not be pretty (Stat-Teaser co-editor Heidi Hansel says, "It's the grossest thing I've seen!"), but children and adults love to squeeze it and throw it around their home or office. For more pictures, chemistry, detailed procedures, historical background (with links), and the Design-Expert data file from my experiments, see http://www.statease.com/playputty.html.
3 - Expert-FAQ: Problems with propagation of error (POE) not being graphed
From: New Jersey
"I have a question about the analysis of a Response Surface Methods (RSM) Design, a Box-Behnken with 3 factors in 15 runs. The response is the conversion of the reaction. The analysis of this response is no problem, but when I want to add the propagation of error (POE), it doesn't work, although I followed the instructions from the Design-Expert User Guide on pages 6-34 and 6-35. As instructed, I entered the standard deviation of the factors and clicked on the model graphs button. But when I tried to select the View for POE it is still grayed out. Can you tell me what is wrong here? Did I forget something, or is something not OK with the software?
My first question was whether you chose a linear model for your response? If so, POE will be constant so the program does not allow it to be graphed. However, this proved not to be the case. The problem was not nearly so obvious: It stems from creating a non-hierarchical model in coded terms:
Y = k + A + B + AB + BC + AC + A^2 + B^2 + C^2
Notice that the non-linear (second order) term C^2 appears in the coded model, but not its parent term C. If you add factor C to the response model, POE works - otherwise, not. POE is calculated on the basis of models in actual terms, which cannot be constructed accurately from non-hierarchical coded models.
Stat-Ease consultant Pat Whitcomb
adds these comments:
"When a polynomial model is well formulated (includes all hierarchically inferior terms) its predictions are invariant (the same) under coding transformations. Design-Expert software calculates the model coefficients using coded factors but it predicts POE using a model for the actual factor levels. (POE requires a model in terms of actual factor levels because the factor standard deviations are entered using actual units of measure.) Therefore the polynomial model has to be invariant to coding transformation to be able to generate POE graphs. For more details on hierarchy see: J. L. Peixoto, 'A Property of Well-Formulated Polynomial Regression Models,' The American Statistician, Feb. 1990, V44, No. 1."
(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 online by linking to the Stat-Ease e-commerce page for workshops.)
4 - Expert-FAQ: More questions about POE - specifically for mixtures, but also in general on impact of variations in input components/factors
From: United Kingdom
"I've got a mixture design where I'm looking to see if addition of various components pays any dividend in terms of the robustness of the formulation. As a few critical responses fit quadratic models and I have a reasonable estimate of standard deviation based on knowledge of plant practice I thought POE would be a good way to get a handle on this. I've followed the procedure as outlined in the User Guide (in the mixture design section) and I've generated my POE surface. My question is this: What difference in the calculated POE value constitutes a practical increase in product robustness? Does the absolute value or difference observed between high points and the plateau on the POE surface tell me whether or not the benefit is of practical significance or not? I'm trying to get my head around what POE represents in practical terms.
For example in one of my responses the values from the model prediction are in the range: 149 to 135 and the POE surface ranges from 2.11 to 2.09 with a clear plateau in the region of higher response value. Does the ratio of POE to response give me some idea of whether there is a tangible benefit in terms of robustness to be gained by moving into the plateau region of the POE trace even though the range of the surface is very small?
My gut instinct is that this is something I should get sorted out with a training course. However, before I can justify that kind of expense I need to try and steer a few uses of POE through my boss to gain some kind of buy in. Any help/advice/reading would be very much appreciated. I am involved in a couple of 6-sigma type activities and so I think it's really important that I get to grips with this concept.
P. S. Congratulations on the "DOE
Simplified" book - its a real boon when trying to get people up and running
with the software."
First of all, I appreciate all compliments on the book I co-authored with Pat Whitcomb (for information on this, see http://www.statease.com/doe_simp.html). You bring up some good questions that relate to the conundrum of statistical significance versus practical importance of effects. For POE, I agree that it makes sense to use the range of response as a benchmark. I suggest dividing the range of POE by the range of response. This might be likened to the coefficient of variation (CV), or percent error, that we report in the post-ANOVA section of our software's data analysis. In your case this "POE CV" does not look too impressive: (2.11-2.09)/(149-135)*100 = 0.33%. It seems likely that this will not be of any practical importance. However, if upon scaleup, all the input factor variations get magnified,
possibly the minimization of POE could become important. In an article written by Pat and me on this topic ("Achieving Six Sigma Objectives for Variability Reduction in Coating Formulation and Processing" at http://makeashorterlink.com/?X1BF219E2), we related the following anecdote on variation in mixture components:
"After earning his Ph.D. in chemistry and taking a job at a chemical company, a colleague of ours got assigned to an operator for an orientation to the real-world of production. As the operator watched with much amusement and disgust, the chemist carefully weighed out materials with a small scoop. The operator pushed the Ph.D. chemist aside, grabbed a sack of chemicals and tossed it into the reactor. "You're not in the laboratory anymore," he said, "This is how we do things in manufacturing."
(Learn more about POE by attending the 3-day computer-intensive workshop "Robust Design, DOE Tools for Reducing Variation." For a complete description see http://www.statease.com/clasrdrv.html. Link from this page to the course outline and schedule. Then, if you like, enroll online.)
5 - Events alert: Aerospace Sciences Meeting in Reno and other places you will find Stat-Ease
Stat-Ease will be represented by DOES Institute http://www.does.org at the 41st American Institute of Aeronautics and Astronautics (AIAA) Aerospace Sciences Meeting and Exhibit this week (January 6-9, 2003) at the Reno Hilton in Reno, Nevada.
Also, we've been asked to pass along
an alert for the Conference on New Directions in Experimental Design to be held
in Chicago, Illinois on May 14-17, 2003. The focus of the conference will be
on design of experiments in the pharmaceutical and related industries. See
(Update 3/07: Link no longer available) for more 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!
6 - Workshop alert: Upcoming classes
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.
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 -
New Year's resolutions from a holy man:
"Life is to live and life is to give and talents are to use for good if you choose.
Do not pray for easy lives,
Pray to be strong.
Do not pray for tasks equal to your powers,
Pray for powers equal to your tasks-
then the doing of your work shall be no miracle but you shall be a miracle."
- Solanus Casey (born in my hometown of Stillwater, Minnesota, this simple, but spiritual, man became a renowned Capuchin (German) Franciscan monk who someday may be declared a Saint.)
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, #2-12 Dec 02, #3-1 Jan 03 (see above)