IN THIS ISSUE: interpreting non-linear blending terms, software update, and more

FAQ

How does negative non-linear blending affect formulation performance?

Original question from a Senior Statistician:

“For a mixture design response where higher is better, I am trying to interpret a negative sign on a two-component nonlinear blend term. I know this means that we have an antagonistic effect, but I wanted to know what this really meant in practical, formulating terms. One AI chat told me that one thing this means is that “increasing these components together is unfavorable.” In other words, increasing the concentration of the pair as a pair (taking percentage from other components) is bad.

“Is this interpretation true? I thought this negative sign only meant that some middle ratio of the two components was bad.”

Answer :
It is good you take this or any AI (artificial intelligence) answer only as a starting point and consult someone with real AI (actual intelligence). You know statistics and I know firsthand how chemicals react and offer an engineering aspect to interpreting models of their performance. That is a positive blend of expertise—synergistic.

I think your interpretation is more precise than the artificially intelligent advisor. To illustrate, I created a thought experiment on milk blended with beer. I tried something like this once with my colleague Tryg when the two of us went for an afterwork brew. The server left a creamer on the table from a previous patron who ordered coffee. I poured some in my beer to see what would happen. I enjoyed watching the dairy product swirl into my alcoholic beverage. However, not surprisingly, it ruined my beer. I reproduced the results by creating a two-component, second degree, simplex lattice, augmented with check blends and replicates—easily done with Stat-Ease software by accepting its defaults for the mixture design. I then ‘dry-labbed’ in the data based on my liking for the taste of milk versus beer versus a blend of the two.

See the response surface plot (speculative) below (higher the better for taste, band showing 95% confidence interval around the fitted curve).

Response surface for milk-beer blend

This picture provides a very helpful visualization of ingredients being antagonistic. It shows equally high liking for pure milk and pure beer (left versus right; respectively), but strong dislike for them being blended.

The coded equation (Scheffé) that creates this predicted response is: R1 = 7.70 A + 8.36 B – 25.4 AB. The big negative coefficient on the nonlinear (second order) blending term AB creates a huge downturn, which hits a minimum at the midpoint. However, though the coding for mixtures on a scale of 0 to 1 works very nicely for interpreting main component effects, it makes the antagonism look far worse than reality. The trick is to multiply its coefficient by one-fourth to assess its downward from the linear blend line. By blending milk with beer, the taste plummets by 6.35 units (=25.4/4)—still very bad, but understandable.

(Learn more about non-linear blending by enrolling in the next Fundamentals of Mixture DOE public workshop - a new, focused offering of just 3.5 hours from me and the training team.)

SOFTWARE

Stat-Ease developers released software version 25.0.4 on October 8. See the Full Changelog for details on the improvements, which include a new feature: The Import Data table now allows renaming of blocks, groups and subgroups. If you use Stat-Ease software and need to identify your current version, do so via Help, About, or simply click Check for Updates.

If you would like a free trial of this latest version of Stat-Ease software, which makes it easier than ever to deploy even more powerful tools for DOE, request it here

EVENTS

Do you need a speaker on DOE for a 2026 learning session within your company or professional society at regional, national, or international levels? If so, please get back to me.

ONLINE LEARNING

Sharpen up your DOE skills with a mix of free and paid training: whatever fits your business needs.

LAST CHANCE: Comprehensive DOE course — Online instructor-led learning

Modern DOE for Process Optimization, 5 half-days, $1295*: December 8-12 - that’s next week!

Our team is moving from week-long, comprehensive courses to short, 3.5 hours courses to help you quickly level up on DOE essentials.  Sign up now for next week’s MDOE workshop if you prefer the old format.

*Only $149 for students, faculty, or researchers at an accredited academic institution. Contact us to qualify.

These new modules will be online, live, and mostly taught by me as we introduce this new mode of learning.

Short courses to quickly level up on DOE essentials — Online instructor-led learning

All courses are 3.5 hours, registration $295**.  Classes will be held in US Central time.

• Introduction to Design of Experiments (DOE)
  Multifactor methods for accelerating process improvement
  Jan 27 9am-12:30pm, Feb 10 1-4:30pm, Mar 24 9am-12:30pm, Apr 14 1-4:30pm

• Basics of Response Surface Methodology (RSM)
  Optimization tools tools for peak process performance
  Feb 12 1-4:30pm, Mar 25 9am-12:30pm

• Fundamentals of Mixture DOE
  Multicomponent methods for rapid formulation development
  Jan 29 9am-12:30pm, Mar 26 9am-12:30pm

• Advanced Tools for Design and Analysis of Experiments
  Making the most from every experiment
  Apr 16, 1-4:30pm

  
  

**Only $95 for students, faculty or researchers. $50 discount per person for enrolling in more than 1 course or by registering multiple people for any given course. Current software or Annual Support & Maintenance subscribers may also ask about an introductory rate. Contact us to qualify.

Don’t see the course you want, or the dates don’t work for you? Ask our team about taking a course asynchronously using recorded video sessions.

See this web page for the complete schedule of upcoming Stat-Ease courses. To enroll in the workshop that suits you best, click Register on that webpage, or click here to contact us.

If you lead a group of six or more colleagues, save money and customize content via a private workshop. For a quote, please contact us.

On-Demand Videos

By the way, our Statistics Made Easy By Stat-Ease YouTube channel provides a free library of highly educational recorded webinars covering a wide variety of DOE tools. It offers videos at all levels—from those new to DOE on up. Take advantage!

INFO

See our latest publication roundup, featuring application of Stat-Ease software for exceptionally successful experiments.

BLOGS

StatsMadeEasy

My wry look at all things statistical and/or scientific with an engineering perspective.

• Today’s Major League Baseball batters all hit below average

• Fresh-made mac and cheese—the ultimate comfort food

• Response surface methods hit the spot for optimizing projectile hurling siege engines

Stat-Ease Blog

Great tips from the Stat-Ease team for making DOE easy, for example, this recent post by me with “Tips and tricks for designing statistically optimal experiments.”

Feel free to get back to me via [email protected] with further questions or comments: I would really appreciate hearing from you!

All the best,

Mark J. Anderson, PE, CQE, MBA
Engineering Consultant, Stat-Ease, Inc.
www.linkedin.com/in/markstat/

QUOTE OF THE DAY

“It is not unusual for a well-designed experiment to analyze itself.”

–Box, Hunter and Hunter, Statistics for Experimenters, 2nd Edition, inside of front cover (along with lots of other great “quaquaversal” quotes there, the next page and inside the back cover).

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