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 email@example.com.
Here's an appetizer to get this Alert off to a good start: Learn how to lay out your lab according to the ancient art of feng shui at http://www.the-scientist.com/yr2003/jul/prof5_030714.html (must have paid subscription to view - this free site offered by The Scientist magazine requires a one-time registration, but this will be time well-spent). I suggest that anyone considering this spiritual approach do some experiments first. About 20 years ago I arrived at a hotel (Marriott?) that had a series of rooms laid out in different ways. For example, one room had a big closet and a little bathroom. The next room had the opposite configurationa little closet and a big bathroom. As I recall, tradeoffs were also made on a couch versus a desk, etc. They paid visitors like me $20 to rate the room according to a number of attributes noted on a written survey. I'd be curious to see if anyone comes up with solid scientific evidence on the benefits of feng shui, particularly as it relates to productivity in a lab or office environment.
Some who practice feng shui may also believe in astrology and lead their lives according to how the planets align. If so, I wonder what they make of Mars being so close to Earth later this month? On August 27, Mars will be within 34,646,418 miles (55,758,006 kilometers) of Earth. This will be the closest that Mars has come to our planet in 60-70 thousand years (estimates vary, but who cares!). See http://www.space.com/spacewatch/where_is_mars.html for details. To determine where Mars (or any other celestial body) will be, go to http://www.skyviewcafe.com/index.php and view the free interactive planetarium (via a Java applet).
Here's what I cover in the body text of this DOE
FAQ Alert (topics that delve into statistical detail are designated
1. Expert-FAQ: Adding replicates to D-optimal factorial designs
[The D-optimal option provides a handy computer-generated
alternative to the traditional fractional factorial because, unlike
two-level designs, it imposes no restrictions on how many "treatments"
you desire. For example, in a case study presented by Stat-Ease in
its Experiment Design Made Easy workshop,
a furniture-maker investigates 5 types of wood veneer with 5 glues
applied 2 ways via 4 clamps tightened at 2 pressures. The 400 combinations
are whittled down to only 77 runs via a D-optimal design geared to
fit all main effects and two-factor interactions. For more details
on D-optimal design see http://www-09.nist.gov/div898/handbook/
If you wish to add replicates you can right click on the button to the left of any row in the design layout and choose to duplicate any point. You can also use Design Tools to write your design as a candidate set. Then choose Design Tools, Augment Design and read in the current design as the candidate set. Edit the model to emphasize the terms of most interest (e.g. choose Main Effects). Put the new experiments into Block 1 and enter the number of additional runs you would like. Since the candidate set contains no new runs the runs selected will be replicates. This method is actually superior to the way it worked in earlier versions of Design-Expert which used the designed-for model to pick the replicates. Since the default for the number of model points is just enough to estimate the model adding replicate points is a random selection. Using augmentation to add replicates picks the points that contribute the most information about the model terms we choose.
Let me emphasize again; adding replicates usually don't contribute as much information as adding new runs. Therefore I'd generally suggest increasing the number of model points in the D-optimal build rather than adding replicates."
(Learn more about factorial designs by attending
the 3-day computer-intensive workshop Experiment Design Made Easy.
for a complete description. Link from this page to the course outline
and schedule. Then, if you like, enroll online.)
2. Expert FAQ: Dealing with inconvenient factor levels from a central composite design for response surface methods (RSM)
If rounding won't get the job done, a more complicated route can be taken: Create a factorial candidate set for a D-optimal design. Under Design Tools, Design-Expert (DX) software offers the "Create Factorial Candidates" feature to help fabricators get do-able design levels. For detailed instructions on this, see page 9-14 of section 9 (Advanced Design Features) in the DX User Guide viewable with Adobe Acrobat Reader in portable document format (PDF) at http://www.statease.com/x6ug/DX09-Features-Design.pdf.
(Learn more about RSM designs 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.)
3. Info alert: See a fun, informative book on the development of science"A Short History of Nearly Everything"
My sister, a medical doctor, sent me this book to pass my time while convalescing from a minor surgery. It's a fascinating journey by a superb writer, Bill Bryson, through the annals of science. I highly recommend it for leisurely reading. See http://physics.miningco.com/cs/bookreviews/gr/AShortHistoryof.htm for details. (Update--3/07: this link has changed to http://geography.about.com/cs/geologictime/gr/aa072803.htm?terms=bill+bryson.) Here's one tidbit tossed out by Bryson that caught my eye. In 1774 a mathematician named Charles Hutton worked on a project to survey Schiehallion mountain in the central Scottish Highlands. The goal was to find its weight for a gravitational experiment aimed at determining the mass of Earth. The surveyors recorded scores of elevations on their map of the mountain. Hutton noticed that by connecting similar values with penciled lines, the slopes and overall shape of the surface became much clearer. Thus, he invented contour lines.
By the way, Hutton calculated the mass of the earth at 5,000 million, million tons. He then deduced the masses of all other major bodies in the solar system, including the sun, at least those known at the time.
One last bit of trivia about planetary bodies:
According to Bryson, in 1781 when William Hershel discovered what
we now call Uranus he wanted to name it "George" after the
British king of that time. Thankfully Hershel was overruled. If you
want to stir things up, make this into a trivia question but try to
keep a straight face and let your listeners consider the obvious,
but off-color, puns.
4. Events alert: Link to a schedule of Stat-Ease appearances
Click on http://www.statease.com/events.html for a list 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: See when and where to learn about DOE
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 J. Anderson, PE, CQE
PS. Quote for the
monthRecollection of Edmond Halley's 1684 visit with Isaac Newton
to learn about the orbit of the planets:
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