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. 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.
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Here's an appetizer to get this Alert off to a good start: Click the "Opportunity Rover Finds an Iron Meteorite on Mars" link at http://marsrovers.jpl.nasa.gov/newsroom/pressreleases/. Looking into this basketball-sized rock, Rover's spectroscopic analysis revealed a chemical composition rarely seen in meteorites that fall on earth. What a robot!
Speaking of robots, here on Earth I bought my son a Roomba® floor vac to police up his place. See an engineer describe the latest Roomba technology by clicking the movie icon at http://www.irobot.com/sp.cfm?pageid=124. I notice they have not yet added a spectroscopic analyzer. Parents could use this for forensics on petrified peas and get after their children who tossed them on the floor rather than eat their vegetables.
Back to outer space, I congratulate the Europeans for the Titanic success (pun intended) of their Space Agency's Huygens probe. See http://www.esa.int/SPECIALS/Cassini-Huygens/SEMEMY71Y3E_0.html.
For a broader view of Titan, plus other moons of Saturn and the planet itself, click the "Cassini Photo Essay" link at http://www.nasa.gov/mission_pages/cassini/main/index.html.
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: Can interactions be larger than main effects?
2. FAQ: Strategy of experimentation for screening
3. Info Alert: Improving Solder-Paste Processes Through DOE
4. Events alert: Link to schedule of appearances by Stat-Ease
5. Workshop alert: See when and where to learn about DOE
PS. Word for the month contributed by statistician Tom Scripps, a trainer for Stat-Ease (http://www.statease.com/tomscrip.html):
"I learned a new word--'apophenia'. It seems to be a concept that fits with the kinds of things to which you refer readers of your newsletter. Look it up." [I did look up this word as you will see at the end of this DOE FAQ Alert. Mark]
"Is it possible for an interaction to have a LARGER effect than either of the parent factors? Is it possible for an interaction to have any kind of effect if neither of the parent factors demonstrate an effect? I've been trying to figure this out on my own."
Yes, as you can imagine from the following examples, an interaction is possible even though neither of the parent factors create significant main effects.
1. In our Experiment Design Made Easy workshop we do a case study on readability of a video display terminal (VDT) with factors:
A. Foreground--black or yellow
B. Background--white or cyan (blue)
The AB interaction predominates because, of course, foreground and background are interdependent.
2. A client of Stat-Ease encountered problems with an integrated chip cleaning process due to:
A. Supplier of chemical 1--company X vs company Y
B. Supplier of chemical 2--company X vs company Y
If either company supplied both chemicals, the process worked, but when both suppliers were included, they interacted badly. Thus the AB interaction was the biggest effect.
What's in common with both these examples is the nature of factors--they are categoric. Categorical factors tend to interact. However, numerical factors can also interact in a big way as shown in Figure 2 at http://www.statease.com/pubs/plastics.pdf. In this case holding pressure (B) combines with cycle time (F) in an injection molding machine to create a large effect on part shrinkage. Neither main effect stands out on the normal plot of effects.
Shari Kraber (http://www.statease.com/sharkrab.html) adds: "Notice how the BF interaction depicted in Figure 2 forms a perfect 'X'. In such cases, the main effect plots of the parent terms (B and F, for example) will be flat lines."
PS. To maintain hierarchy, we recommend you keep both the 'parents' of a two-factor interaction in your factorial model. For the statistical reasons, refer to FAQ #3 in my April 2003 Alert at http://www.statease.com/news/faqalert3-4.html. However, as a practical matter, it would not make sense to say that either parent makes no difference when together they create such a large effect. For example, in the VDT case, how could you read the screen without both the foreground and the background?
(Learn more about interactions by attending the three-day computer-intensive workshop "Experiment Design Made Easy." See http://www.statease.com/clas_edme.html for a course description. Link from this page to the course outline and schedule. Then, if you like, enroll online.)
From: P. B. Dhanish, Lecturer, Department of Mechanical Engineering, National Institute of Technology, Calicut, India
"This is regarding the excerpt from Chapter 1 of "RSM Simplified" [at http://www.statease.com/pubs/rsmsimpexcerpts--chap1.pdf]. In Figure 1-1 Strategy of Experimentation, you recommend that Known Factors need not be included in a screening design. If among the Unknown Factors, one factor has no effect by itself, but has an interaction with the Known Factor, then we will miss out on this factor completely. Hence, is this an advisable strategy?"
This is a question I've debated over with other experts on DOE. Of course you are correct that by first screening the trivial many factors from the vital few among those previously not studied (unknown), an experimenter runs the risk of overlooking an important interaction. However, by temporarily setting aside
known factors, the screening probably can be done more efficiently and with greater sensitivity. Otherwise, the factors already known to create big effects on the response will be needlessly confirmed and possibly overwhelm smaller effects that had never before been discovered.
P.S. My co-author Pat suggested I remind you that in our "RSM Simplified" book we advise that screening be done with Resolution IV designs that will not resolve interactions, so it really makes no sense in this case to worry about them at this stage. Thus, temporarily holding off the 'known' factors is apropos. However, if an experimenter wants to resolve interactions between any of the possible variables, they could skip the screening stage and go directly to "breakthrough" where they run Resolution V designs. The
disadvantage of this approach is that the experiments become very large due to the many factors and the need to resolve all the two-factor interactions. A new class of designs called minimum-run Resolution V designs may make this more palatable. See http://www.statease.com/pubs/small5.pdf for details.
(See http://www.statease.com/rsm_simplified.html for details on the new book "RSM Simplified: Optimizing Processes Using Response Surface Methods for Design of Experiments" by Mark J. Anderson and Patrick J. Whitcomb. It comes with a free 180-day trial version of Design-Expert® version 7 DOE software.)
The December issue of Surface Mount Technology (SMT) features an article by Bill Craig on DOE. Proper application of solder paste onto a printed circuit board (PCB) is essential in surface mount assemblies. Bill's article examines a screening design which ultimately improved electrical yields. For details, see
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 private class at your site. Call us to get a quote.
I hope you learned something from this issue. Address your general questions and comments to me at: Mark@StatEase.com.
Mark J. Anderson, PE, CQE
PS. Word for the month: 'Apophenia'
--I found this definition via a free Web-based encyclopedia: "Apophenia is the experience of seeing patterns or connections in random or meaningless data. The term was coined in 1958 by Klaus Conrad, who defined it as the "unmotivated seeing of connections" accompanied by a "specific experience of an abnormal meaningfulness...In statistics, apophenia would be classed as a Type I error."
Should I read something into Tom's mention of this word? Is he trying to tell me something? Am I being an apopheniac?
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DOE FAQ Alert—Copyright 2005
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