Issue: Volume 3, Number 8
Date: August 2003
From: Mark J. Anderson, Stat-Ease, Inc. (

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 If this newsletter prompts you ask to your own questions about DOE, please address them to

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 (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 configuration—a 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 for details. To determine where Mars (or any other celestial body) will be, go to 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 "Expert"):

1. Expert-FAQ: Adding replicates to D-optimal factorial designs
2. Expert-FAQ: Dealing with inconvenient factor levels from a central composite design for response surface methods (RSM)
3. Info alert: See a fun, informative book on the development of science—"A Short History of Nearly Everything"
4. Events alert: Link to a schedule of Stat-Ease appearances
5. Workshop alert: See when and where to learn about DOE

PS. Quote for the month
—Recollection of Edmond Halley's 1684 visit with Isaac Newton to learn about the orbit of planets


1. Expert-FAQ: Adding replicates to D-optimal factorial designs

-----Original Question-----
From: New York

"I noticed when you select a D-optimal factorial design in your most current versions of Design-Expert® software it no longer adds replicated runs by default. Is there a reason for this?"

[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

Answer (from Stat-Ease consultant Pat Whitcomb):
"The D-optimal routine for fractionating factorials was cloned from the one for used for building response surface designs. In response surface designs enough points are selected to estimate the full approximating polynomial (e.g. a 2nd order polynomial), then additional points are added to estimate lack-of-fit and finally replicates are added to estimate pure error. When fractionating a factorial we don't have enough points to estimate the full factorial model. In this case adding new factorial points usually will provide more information than replicating existing points. Due to sparsity of effects there are usually enough runs to estimate error without replicates. Therefore we removed the replicate field from the D-optimal routine for building fractional factorials.

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. See 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)

-----Original Question-----
From: Alabama

"What do we do when a central composite design (CCD) specifies a combination for the response surface that simply can not be fabricated because of material/physics of the situation?"

First of all, don't be afraid to round the specified values a bit for the sake of convenience. For example, I notice that the axial points (typically drawn as stars in textbooks covering CCDs) for the micron (thickness?) in your design are specified at 4.89 and 30.11 (versus the factorial range of 10 to 25). Could you hit 4 and 32, or 5 and 30? Also, I see that the center-point comes out at 17.5. I'd be a bit more circumspect about changing this level because it's literally a central building block in the CCD.

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

(Learn more about RSM designs by attending the Response Surface Methods for Process Optimization workshop. For a description, see 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 for details. (Update--3/07: this link has changed to 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 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

See 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
Principal, Stat-Ease, Inc. (
Minneapolis, Minnesota USA

PS. Quote for the month—Recollection of Edmond Halley's 1684 visit with Isaac Newton to learn about the orbit of the planets:

"Dr. Halley came to visit [Sir Isaac Newton] at Cambridge [and]...asked him what he thought the curve would be that would be described by the Planets supposing the force of attraction toward the sun to be reciprocal to the square of their distance from it. Sr. Isaac replied immediately that it would be an [ellipse]. The Doctor, struck with joy & amazement, asked him how he knew it. 'Why,' saith he, 'I have calculated it,' whereupon Dr. Halley asked him for his calculation without further delay, Sr. Isaac looked among his papers but could not find it."

—Abraham DeMoivre (recounted in "A Short History of Nearly Everything" on page 47)

Trademarks: Design-Ease, Design-Expert and Stat-Ease are registered trademarks of Stat-Eae, 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 for resumes)
—Statistical advisor to Stat-Ease: Dr. Gary Oehlert (
—Stat-Ease programmers, especially Tryg Helseth (
—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, #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 (see above)

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