Stat-Ease Blog


Strategy of Experiments for Formulations: Try Screening First!

posted by Mark Anderson on Oct. 26, 2022

Consider Screening Down Components to a Vital Few Before Studying Them In-Depth

At the outset of my chemical engineering career, I spent 2 years working with various R&D groups for a petroleum company in Southern California. One of my rotations brought me to their tertiary oil-recovery lab, which featured a wall of shelves filled to the brim with hundreds of surfactants. It amazed me how the chemist would seemingly know just the right combination of anionic, nonionic, cationic and amphoteric varieties to blend for the desired performance. I often wondered, though, whether empirical screening might have paid off by revealing a few surprisingly better ingredients. Then after settling in on the vital few components doing an in-depth experiment may very well have led to discovery of previously unknown synergisms. However, this was before the advent of personal computers and software for mixture design of experiments (DOE), and, thus, extremely daunting for non-statisticians.

Nowadays I help many formulators make the most from mixture DOE via Stat-Ease softwares’ easy-to-use statistical tools. I was very encouraged to see this 2021 meta-analysis that found 200 or so recent publications (2016-2020) demonstrating the successful application of mixture DOE for food, beverage and pharmaceutical formulation development. I believe that this number can be multiplied many-fold to extrapolate these findings to other process industries—chemicals, coatings, cosmetics, plastics, and so forth. Also, keep in mind that most successes never get published—kept confidential until patented.

However, though I am very heartened by the widespread adoption of mixture DOE, screening remains underutilized based on my experience and a very meager yield of publications from 2016 to present from a Google-Scholar search. I believe the main reasons to be:

  • Formulators prefer to rely on their profound knowledge of the chemistry for selection of ingredients (refer to my story about surfactants for tertiary oil recovery)
  • The number of possibilities get overwhelming; for example, this 2016 Nature publication reports that experimenters on a pear cell suspension culture got thrown off by the 65 blends they believed were required for simplex screening of 20 components (too bad, as shown in the Stat-Ease software screenshot below, by cutting out the optional check blends and constraint-plane-centroids, this could be cut back to substantially.)
  • Misapplying factorial screening to mixtures, which, unfortunately happens a lot due to these process-focused experiments being simpler and more commonly used. This is really a shame as pointed out in this Stat-Ease blog post

I feel sure that it pays to screen down many components to a vital few before doing an in-depth optimization study. Stat-Ease software provides some great options for doing so. Give screening a try!!

For more details on mixture screening designs and a solid strategy of experiments for optimizing formulations, see my webinar on Strategy of Experiments for Optimal Formulation. If you would like to speak with our team about putting mixture DOE to good use for your R&D, please contact us.

Wrap-Up: Thanks for a great 2022 Online DOE Summit!

posted by Rachel Poleke on Oct. 10, 2022

Thank you to our presenters and all the attendees who showed up to our 2022 Online DOE Summit! We're proud to host this annual, premier DOE conference to help connect practitioners of design of experiments and spread best practices & tips throughout the global research community. Nearly 300 scientists from around the world were able to make it to the live sessions, and many more will be able to view the recordings on the Stat-Ease YouTube channel in the coming months.

Due to a scheduling conflict, we had to move Martin Bezener's talk on "The Latest and Greatest in Design-Expert and Stat-Ease 360." This presentation will provide a briefing on the major innovations now available with our advanced software product, Stat-Ease 360, and a bit of what's in store for the future. Attend the whole talk to be entered into a drawing for a free copy of the book DOE Simplified: Practical Tools for Effective Experimentation, 3rd Edition. New date and time: Wednesday, October 12, 2022 at 10 am US Central time.

Even if you registered for the Summit already, you'll need to register for the new time on October 12. Click this link to head to the registration page. If you are not able to attend the live session, go to the Stat-Ease YouTube channel for the recording.


Want to be notified about our upcoming live webinars throughout the year, or about other educational opportunities? Think you'll be ready to speak on your own DOE experiences next year? Sign up for our mailing list! We send emails every month to let you know what's happening at Stat-Ease. If you just want the highlights, sign up for the DOE FAQ Alert to receive a newsletter from Engineering Consultant Mark Anderson every other month.

Thank you again for helping to make the 2022 Online DOE Summit a huge success, and we'll see you again in 2023!

Experimental Design in Chemistry: A Review of Pitfalls (Guest Post)

posted by James Cawse on Nov. 1, 2019

This blog post is from James Cawse, Consultant and Principal at Cawse and Effect, LLC. Jim uses his unique blend of chemical knowledge, statistical skills, industrial process experience, and quality commitment to find solutions for his client's difficult experimental and process problems. He received his Ph.D. in Organic Chemistry from Stanford University. On top of all that, he's a great guy! Visit his website (link above) to find out more about Jim, his background, and his company.


Getting the best information from chemical experimentation using design of experiments (DOE) is a concept that has been around for decades, although it is still painfully underused in chemistry. In a recent article Leardi1 pointed this out with an excellent tutorial on basic DOE for chemistry. The classic DOE text Statistics for Experimenters2 also used many chemical illustrations of DOE methodology. In my consulting practice, however, I have encountered numerous situations where ’vanilla‘ DOE – whether from a book, software, or a Six Sigma course – struggles mightily because of the inherent complications of chemistry.

The basic rationale for using a statistically based DOE in any science are straightforward. The DOE method provides:

  • Points distributed in a rational fashion throughout “experimental space”.
  • Noise reduction by averaging and application of efficient statistical tools.
  • ‘Synergy’, typically the result of the interactions of two or more factors - easily determined in a DOE.
  • An equation (model) that can then be used to predict further results and optimize the system.
All of these are provided in a typical DOE, which generally starts simply with a factorial design.

DOE works so well in most scientific disciplines because Mother Nature is kind. In general:

  • Most experiments can be performed with small numbers of ’well behaved‘ factors, typically simple numeric or qualitative at 2-3 levels
  • Interactions typically involve only 2 factors. Three level and higher interactions are ignored.
  • The experimental space is relatively smooth; there are no cliffs (e.g. phase changes).
As a result, additive models are a good fit to the space and can be determined by straightforward regression.

Y = B0 + B1x1 + B2x2 + B12x1x2 + B11x12 +…

In contrast, chemistry offers unique challenges to the team of experimenter and statistician. Chemistry is a science replete with nonlinearities, complex interactions, and nonquantitative factors and responses. Chemical experiments require more forethought and better planning than most DOE’s. Chemistry-specific elements must be considered.


Above all, chemists make mixtures of ‘stuff’. These may be catalysts, drugs, personal care items, petrochemicals, or others. A beginner trying to apply DOE to a mixture system may think to start with a conventional cubic factorial design. It soon becomes clear, however, that there is an impossible situation when the (+1, +1, +1) corner requires 100% of A and B and C! The actual experimental space of a mixture is a triangular simplex. This can be rotated into the plane to show a simplex design, and it can easily be extended to high dimensions such as a tetrahedron.

It is rare that a real mixture experiment will actually use 100% of the components as points. A real experiment with be constrained by upper and lower bounds, or by proportionality requirements. The active ingredients may also be tiny amounts in a solvent. The response to a mixture may be a function of the amount used (fertilizers or insecticides, for example). And the conditions of the process which the mixture is used in may also be important, as in baking a cake – or optimizing a pharmaceutical reaction. All of these will require special designs.

Fortunately, all of these simple and complex mixture designs have been extensively studied and are covered by Cornell3, Anderson et al4, and Design-Expert® software.


The goal of a kinetics study is an equation which describes the progress of the reaction. The fundamental reality of chemical kinetics is

Rate = f(concentrations, temperature).

However, the form of the equation is highly dependent on the details of the reaction mechanism! The very simplest reaction has the first-order form

Rate = k*C1

which is easily treated by regression. The next most complex reaction has the form

Rate = k*C1*C2

in which the critical factors are multiplied – no longer the additive form of a typical linear model. The complexity continues to increase with multistep reactions.

Catalysis studies are chemical kinetics taken to the highest degree of complication! In industry, catalysts are often improved over years or decades. This process frequently results in increasingly complex catalyst formulations with components which interact in increasingly complex ways. A basic catalyst may have as many as five active co-catalysts. We now find multiple 2-factor interactions pointing to 3-factor interactions. As the catalyst is further refined, the Law of Diminishing Returns sets in. As you get closer to the theoretical limit – any improvement disappears in the noise!

Chemicals are not Numbers

As we look at the actual chemicals which may appear as factors in our experiments, we often find numbers appearing as part of their names. Often the only difference among these molecules is the length of the chain (C-12, 14, 16, 18) and it is tempting to incorporate this as numeric levels of the factor. Actually, this is a qualitative factor; calling it numeric invites serious error! The correct description, now available in Design-Expert, is ’Discrete Numeric’.

The real message, however, is that the experimenters must never take off their ’chemist hat‘ when putting on a ’statistics hat’!

Reference Materials:

  1. Leardi, R., "Experimental design in chemistry: A tutorial." Anal Chim Acta 2009, 652 (1-2), 161-72.
  2. Box, G. E. P.; Hunter, J. S.; Hunter, W. G., Statistics for Experimenters. 2nd ed.; Wiley-Interscience: Hoboken, NJ, 2005.
  3. Cornell, J. A., Experiments with Mixtures. 3rd ed.; John Wiley and Sons: New York, 2002.
  4. Anderson, M.J.; Whitcomb, P.J.; Bezener, M.A.; Formulation Simplified; Routledge: New York, 2018.