Stat-Ease | The DOE FAQ Alert Vol. 13 No. 4

PS. Quote for the month: Thought-provoking observation by the late George Box on the need to challenge models based on meager data.

From an Process Engineer:
“I’m looking for one-third fraction of a three-level design on three factors.”

“Design-Expert® explicitly provides better three-level options such as the central composite design (CCD) and Box-Behnken to fill this niche. However, here is a work-around if you really want this 3³-1 layout—under the Response Surface tab, Miscellaneous, build the full-factorial design (3³) with three blocks of 9 runs each. Then delete all but one of these blocks. However this leaves you with a 9-run experiment that cannot estimate all the terms in the quadratic model—the standard for response surface methods (RSM). You will be able to fit a two-factor interaction (2FI) model, but not any pure curvature in the system.

I suggest you consider a full two-level factorial design (2³) with 4 center points. This 12-run experiment will fit the 2FI model and also detect curvature. If curvature turns out to be an issue, you can then augment the design to a CCD.”

P.S. Coincidentally, about the same time this question came in another one was posed by a chemistry professor wanting to set up a 3⁴-1 design. Wayne gave similar advice to build the full design with blocks and then pick one—discarding the other blocks. With the extra factor (four versus three), this 27-run fractional three-level design is capable of fitting the full quadratic RSM model, but a Box-Behnken or face-centered central composite design (FCD) would be preferable.
—Mark

(Learn more about factorial designs with center points by attending the two-day computer-intensive workshop Experiment Design Made Easy. Click on the title for a description of this class and link from this page to the course outline and schedule. Then, if you like, enroll online.)

2: Expert FAQ: How far out should one go when looking for the optimum for a central composite design (CCD) for response surface methods (RSM)?

From a Professor of Engineering Technology:
“My class performed a CCD using a weight-driven trebuchet, which is only slightly different than the typical rubber-band driven catapults that are common. This CCD used the placement of the cup along the throwing arm and the angle of release as the two factors. The settings were entered as +/- 1 levels and not as alphas. I am analyzing the experiment using Design-Expert software.

When we use numerical optimization, the settings for the factor level limits are the levels for the factorial. It seems like the software should know that we ran some trials at the alpha limits and those should be what are used for the limits. When I set the limits to match the settings for the alpha trials, the predicted value is substantially higher ("farther is better" for this experiment). So...here is my question: Why are the default values for the factor limits set at the factorial levels, instead of the alpha levels, when using numerical optimization? Thank you very much!”

“The interval estimates at the axial ranges can be quite wide, too wide to safely predict when all factors reach this extreme limit as shown in the figure below (note the big increase in standard error at the corners!).

However, Design-Expert does offer a clever way to push out to the alpha points by restricting the region within the standard error at these far-out experimental conditions. In the numerical optimization specification expand the range of the factors to the alpha limits, which is easiest to do with Display Options for Process Factors in Coded levels (1.414 for k=2 CCD). Then, for Options, enable “Include standard error models”.

You will get an extra response called “StdErr” in the criteria window. As always, the upper limit is the highest observed (or in this case computed) value at the design points, including the axial runs. Leaving the settings as-is will keep the search within the axial points and spaces outside the factorial box that do not exceed the standard error at these extremes.

(Learn more about central composite designs by attending the two-day computer-intensive workshop Response Surface Methods for Process Optimization. Click on the title for a description of this class and link from this page to the course outline and schedule. Then, if you like, enroll online.)

The June issue of BioProcess International features a fine overview of “Microscale Analysis and DoE, which credits Stat-Ease for publishing the first personal-computer program dedicated to this powerful tool for biopharma researchers. : )

My colleague, Wayne Adams, and I recently presented educational webinars on DOE for QbD. See my talk, done for the American Society of Quality (ASQ) Statistics Division, here and Wayne’s presentation, provided by Stat-Ease, via this link.

5: Events alert: Statistics in Business and Industry Meeting and World Statistics Congress (WSC) this August in Hong Kong

On August 24, I will give a talk on “Practical Aspects for Designing Statistically Optimal Experiments” at the International Statistical Institute Satellite Meeting prior to the WSC in Hong Kong. See the program and register here. This meeting is sponsored by the International Society for Business and Industrial Statistics (ISBIS). Stop by and visit us at booth 22 at WSC.

All classes listed below will be held at the Stat-Ease training center in Minneapolis unless otherwise noted. If possible, enroll at least 4 weeks prior to the date so your place can be assured. Also, take advantage of a $395 discount when you take two complementary workshops that are offered on consecutive days.

**Take both EDME and MIX in the same week to earn $395 off the combined tuition!
***Take both MIX and MIX2 in the same week to earn $395 off the combined tuition!

See this web page for complete 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 Shari at 612-746-2035. 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. Once you achieve a critical mass of about 6 students, it becomes very economical to sponsor a private workshop, which is most convenient and effective for your staff. For a quote, e-mail workshops@statease.com.

I hope you learned something from this issue. Address your general questions and comments to me at: mark@statease.com.

Please do not send me requests to subscribe or unsubscribe—follow the instructions at the end of this message. Sincerely,

PS. Quote for the month—Thought-provoking observation by the late George Box on the need to challenge models based on meager data:

"
An interesting problem occurs when several mechanisms lead to different sets of differential equations. I became aware of this problem while attending a Ph.D. final for one of the chemical engineers. He’d run some experiments which, he said, did not contradict the model—which was true, they didn’t contradict the model—but they also didn’t contradict almost any other model you’d like to name. If you think of a bunch of experiments that produce data which don’t cover much of a range then you can put all kinds of lines through them. So what I decided to think about was how do you test a model, and how do you run experiments that put a model in jeopardy.”

—George Box (Source: “A Conversation with George Box” by Morris H. DeGroot, Statistical Science, V2, #3 (1987), 239-258.

Trademarks: Stat-Ease, Design-Ease, Design-Expert and Statistics Made Easy are registered trademarks of Stat-Ease, Inc.

Acknowledgements to contributors:
—Students of Stat-Ease training and users of Stat-Ease software
—Stat-Ease consultants Pat Whitcomb, Shari Kraber, Wayne Adams and Brooks Henderson
—Statistical advisor to Stat-Ease: Dr. Gary Oehlert
—Stat-Ease programmers led by Neal Vaughn
—Heidi Hansel Wolfe, Stat-Ease sales and marketing director, Karen Dulski, and all the remaining staff that provide such supreme support!