Mixture and Combined Designs for Optimal Formulations (MIXC), $1695

In this 3-day computer-intensive workshop, formulators learn how to use mixture designs to develop statistical models of product performance. Then they use regression analysis and optimization to explore their formulations and identify the "sweet spot" where all specifications can be met. Experimenters will: set up simplex designs, select appropriate mixture models, generate contour plots in triangular space, design for constrained mixture variables, optimize product formulas, and study mixture and process variables.

Attend the first 2 days only at a reduced rate. Please inquire for this option.

* Includes a $95 fee for workshop materials which is subject to state and local taxes.

A 10% discounted Early Bird rate applies to registrations made 6 weeks prior to the workshop date.

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Price: $1,535.00

Mixture and Combined Designs for Optimal Formulations (MIXC), $1695


Mixture and Combined Designs for Optimal Formulations (MIXC) (2 or 3 days)

The Recipe for Success

If you do product formulation, then standard factorial designs just don't work. You need mixture designs to experiment most effectively. When your work involves both changing the formulation and processing the product, mixture-process combined designs are the optimal tool for success.

Ingredients for Efficient Experimentation

During the Mixture and Combined Designs for Optimal Formulations workshop you will:

  • Discover what defines a mixture experiment
  • Set up simplex designs
  • Augment and evaluate design quality
  • Select appropriate mixture models
  • Generate contour plots in triangular space
  • Design for constrained mixture variables
  • Optimize product formulas
  • Combine mixture and process variables
  • Deal with hard-to-change factors using split-plot designs
  • Improve process understanding with mixture-amount, mixture-categoric, and combined-mixture designs

"Very knowledgeable and helpful instructors."
—Rich Griffin, Research Chemist

Produce Contour Maps in Mixture Space

Design-Expert® software helps you practice designing and analyzing mixture experiments throughout the workshop. The software provides the power for the generation of optimal designs, as well as sophisticated graphical outputs such as trace plots. You will learn how these methods work and what to look for.

Course Outline

Day 1

Section 1 – Introduction to Mixtures

  • What makes a mixture?
  • Mixture (Scheffé) polynomials
  • Gold jewelry

Section 2 – Unconstrained Mixtures

  • Simplex-Lattice designs
    • Simplex without augmentation
    • Augmenting simplex designs
      • Augmented simplex lattice: Yarn
  • Blocking a simplex design: Olive oil


Section 3 – Constrained Mixtures, Simplex

  • Detergent formulation
    • Coding: Actual – Real – L_Pseudo
    • Build & analyze
  • Optimization of Multiple Responses
    • Numeric (desirability function)
  • ABS pipe
    • Model reduction
    • Optimization
    • Piepel's vs Cox'x direction
    • Graphical (overlay plot)

Section 4 – Constrained Mixtures, Non-Simplex

  • Sizing for precision
  • Constrained mixtures, extreme vertices: Shampoo
 Day 2

Section 5 – Optimal Designs

  • Optimal point selection: Hydrophilic tablet
  • Transformations & equation only: Antiseptic
Lunch Section 6 – Multicomponent Linear Constraints
  • MLC primer
  • Group constraints: Fruit punch
  • Ratio constraints: Stability
  • An additional equality constraint: Ice cream
  • Selecting a metric for components: Polyols

Section 7 – Screening Components

  • Simplex: Gasoline additives
  • Non-simplex screening designs - exercise and follow-up study

Section 8 – Quality by Design - QbD (optional material as time allows)

  • Quality by Design - QbD
    • Tolerance interval back off
  • Illustrative QbD example: Transdermal drug delivery
 Day 3  Section 1 – Combining Mixture and Process Variables
  •  Combined designs
    • Fish patties (user defined)
    • Fish patties (optimal)
   Section 2 – Mixture Amount & Mixtures with Categoric Factors
  • Mixture amount experiment: Ibuprofen
  • Mixtures with categoric factors:Composite material
  • Categoric factors with proportion going to zero: Shelf life
   Section 3 – Combining Mixture and Process Variables as Split Plots
  • Combined split-plot designs
    • Reverse phase HPLC (split plot - process HTC)
    • Sweet Potato Chips (split plot - mixture HTC) 
   Section 4 – Combining Mixture Designs
  • Combining two mixtures: Nutrient solution
  • Two mixture and an amount: Lady Baltimore cake
    • Limiting combined order for base model
 Lunch  Section 5 – KCV Model: Combining Mixture and Process Variables
  • Background
  • Example (3M+2P)
  • Exercise: Corndogs
   Section 6 – Augmenting Mixture Design
  • Augmenting a mixture design
    • For larger DOE space: Suncreen
    • For higher order model: Sparklers
   Section 7 – Summary and Special Topics (optional)
  • Summary
    • Exercise: Optimize your formulation
    • Next Steps
  • Special Topic (as time allows)
    • Partial Quadratic Mixture (PQM) models
      • Linear with subset of squared and cross product terms
      • Waste Glass Durability
   Section 8 – Appendix
  • Categoric factors with proportion going to zero
    • What's the problem?
    • Shelf life example
    • Additional reference material
  • Using Ratios of Components
    • Ratios as a natural scale
    • Using ratios to combine designs


What if I don’t know whether I need this class?
We encourage you to read our free download, "A Primer on Mixture Design: What’s In It for Formulators?". This introductory text offers formulators modern insights into experimentation on formulations. Learn how mixture designs will meet your needs and produce better results than factorial designs.

Additional Information

PDHs 24 (equals 2.4 CEUs)
Additional Information

Workshop location details will be provided with your confirmation letter, which will be sent once minimum enrollment requirements are met.

Past workshops have been held at the following addresses:

Minneapolis, MN (Stat-Ease headquarters): 2021 East Hennepin Ave, Suite 480, Minneapolis, MN 55413

Edison, NJ: Raritan Plaza III, 105 Fieldcrest Avenue, Suite 201, Edison, New Jersey 08837, Web site

San Diego, CA: 350 10th Avenue, Suite 950, San Diego, California 92101, Web site 

San Jose, CA: 2025 Gateway Place, Suite 390, San Jose, California 95110, Web site 

Recommended Texts and Software

Recommended Texts and Software

Purchase the recommended software at the time of registration to receive a 20% discount. Formulation Simplified text may be purchased at a 20% discount in conjunction with the workshop registration. Other recommended texts may be purchased from your favorite bookseller.