Topics in the body text of this DOE FAQ Alert are headlined below (the "Expert" ones, if any, delve into statistical details):

P.S. Quote for the month: Aiming for the truth (rather than wishful thinking).

(Page down to the end of this e-zine to enjoy the actual quote.)

1: FAQ: How to create an overlay plot that frames in your sweet spot—the factor (design) space where the process meets all response goals

Original Question from a Principal Scientist—Product Development:
“I completed an optimization experiment using the response surface method (RSM) tools in Design-Expert® software for design and analysis. It went very well, producing good predictive models for my critical responses. The numerical optimization gave me the most desirable factor levels, that is, the optimal point to operate the process. However, I want to produce an overlay plot to see how robust this solution will be. How do I do this?”

Answer from Stat-Ease Consultant Wayne Adams:
“As you can see in the figure below, the overlay plot comes up by clicking the Graphical node under Optimization. By completing the numerical optimization beforehand, you are presented with the most desirable setup of factors, with the operating window (also known as the “sweet spot”) framed by your acceptable ranges. In this case we asked Design-Expert to show the one-sided confidence intervals (CIs), which push in the sweet spot from the absolute boundaries—these being subject to uncertainty due to experimental error.”

Graphical optimization (overlay) plot with most desirable process set-up flagged and CI’s imposed

(Learn more about response surface methods by attending the three-day computer-intensive workshop on Modern DOE 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.) 

2: FAQ: When a mixture (or process) space is narrowly constrained, does it make sense to design for anything beyond a linear model?

Original question from a Senior Statistician:
“Mark, the design space for a 3-component mixture-experiment is constrained to a very narrow rectangle along the left side of the ternary diagram. Should we still aim for a quadratic model (the default in Design-Expert) for our optimal design, or would a linear model suffice?”

Answer:
It does seem as though your space is so narrow that everything must line up. However, the quadratic remains a strong possibility. For example, observe the big curve in the figure below. It shows foam height as a function of three surfactants varied in a shampoo. Surfactant C, being very active, was kept to a narrow range. Even so, it generated a nonlinear effect.

A quadratic response surface

As this case study illustrates, the shape of the experimental region has no bearing on the perplexing question of what model to choose for your optimal design. This requires subject matter expertise. As noted by me (and Pat Whitcomb) in Practical Aspects for Designing Statistically Optimal Experiments (Journal of Statistical Science and Application 2 (2014) 85-92), industrial experimenters generally choose a quadratic polynomial. However, based on my experience as a chemical engineer, when dealing with mixtures of highly interactive components such as surfactants, going to the special cubic order* may be advisable, provided it does not increase the number of blends beyond the budget of materials, time or cost.
—Mark

*For details on this crafty model, see the Chapter 2 Appendix: “The Special Cubic” in the Primer on Mixture Design: What’s In It for Formulators? by me and Pat.

(Learn more about mixture design by attending the computer-intensive three-day workshop Mixture and Combined Designs for Optimal Formulations. Click on the title for a complete description of this class. Link from this page to the course outline and schedule. Then, if you like, enroll online.)

3: Book giveaway: Win a free, autographed DOE Simplified or RSM Simplified book!

(Sorry, due to the high cost of shipping, this offer applies only to residents of the United States and Canada.)

Simply reply to this e-mail by February 15 if you’d like a chance at getting a free, DOE Simplified or RSM Simplified book,* autographed by my co-author Pat Whitcomb and me. Good luck!

*(These come from a limited overstock of prior editions—still very useful to learn about design of experiments and response surface methods, but some years behind our latest and greatest versions, which you can purchase via the Stat-Ease publications site here.)

4: Events alert: “Smart Data: Design of Experiments” session coming to D.C. area (2nd notice)

(Second notice) I will co-chair a session on “Smart Data: Design of Experiments” and, there, give a talk on “Ruggedness Testing Made Easier with Graphical Effects Analysis” for IFPAC 2017 in Arlington, VA, (Washington, D.C.) February 27–March 3. This conference gathers technical professionals seeking tools for process analytical technology (PAT), quality by design (QbD), and real-time analytics. Register for IFPAC 2017 here.

Click here for these and other upcoming appearances by Stat-Ease professionals.

P.S. Do you need a speaker on DOE for a learning session within your company or technical society at regional, national, or even international levels? If so, contact me. It may not cost you anything if Stat-Ease has a consultant close by, or if a web conference will be suitable. However, for presentations involving travel, we appreciate reimbursement for travel expenses. In any case, it never hurts to ask Stat-Ease for a speaker on this topic.

5: Workshop alert: See when and where to learn about DOE—Sign up now before classes fill

You can do no better for quickly advancing your DOE skills than attending a Stat-Ease workshop. In these computer-intensive classes, our expert instructors provide you with a lively and extremely informative series of lectures interspersed by valuable hands-on exercises with one-on-one coaching. Enroll at least 6 weeks prior to the date so your place can be assured—plus get a 10% “early-bird” discount.

• DOE Simplified: Half-Day Workshop (DOESH)*
  *New! This dynamic half-day workshop will open your eyes to the power of design of experiments and demonstrate the tools you need to achieve breakthrough improvements in your processes and create superior products.
• April 6, Minneapolis, Minnesota (MN)
  
  
• Experiment Design Made Easy (EDME)
• April 3–4, San Jose, California (CA)
  
  
• Modern DOE for Process Optimization (MDOE)*
  *New! In one three-day class, master the entire strategy of experimentation from screening, characterization to optimization using factorial designs and response surface methods (RSM).
• June 20–22, Minneapolis, Minnesota (MN)
  
  
• Mixture and Combined Designs for Optimal Formulations (MIXC)
• February 22–24, Minneapolis, Minnesota (MN)
  
  
• Designed Experiments for Pharma (DEPH)
• May 15–16, Edison, New Jersey (NJ)

See this web page for a complete schedule and site information on all Stat-Ease workshops open to the public. To enroll, you can either scroll down to the workshop of your choice and click on it, e-mail our Client Specialist Rachel Pollack at [email protected], or call 612-746-2030. 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 [email protected].

I hope you learned something from this issue. Address your general questions and comments to me at: [email protected].

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

Sincerely,

Mark

Mark J. Anderson, PE, CQE
Principal, Stat-Ease, Inc.
2021 East Hennepin Avenue, Suite 480
Minneapolis, Minnesota 55413 USA

P.S. Quote for the month—aiming for the truth (rather than wishful thinking):

"Our aim as scientists is objective truth; more truth, more interesting truth, more intelligible truth. We cannot reasonably aim at certainty. Once we realize that human knowledge is fallible, we realize also that we can never be completely certain that we have not made a mistake.”
—Karl Popper (generally regarded as one of the greatest philosophers of science of the 20th century and the progenitor of the null hypothesis.)

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 Martin Bezener
—Statistical advisor to Stat-Ease: Dr. Gary Oehlert
—Stat-Ease programmers led by Neal Vaughn
—Heidi Hansel Wolfe, Stat-Ease sales and marketing director, and all the remaining staff that provide such supreme support!

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