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

In this new  3-day computer-intensive workshop, formulators learn how to use mixture designs to develop statistical models of product performance. Then they will 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 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

Newly offered in 2016 to incorporate state-of-the-art tools for mixtures! 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
  • Inverted simple U_Pseudo

Section 4 – Optimization of Multiple Responses

  • Detergent formulation (revisited)
    • Numeric (desirability function)
    • Graphical (overlay plot)
  • ABS pipe
    • Model reduction
    • Optimization
    • Piepel’s vs. Cox’s direction
 Day 2

Section 5 – Constrained Mixtures, Non-Simplex

  • Sizing for precision
  • Constrained mixtures, extreme vertices: Shampoo
    • 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 – Quality by Design - QbD (optional material as time allows)

  • Quality by Design - QbD
    • Tolerance interval back off
  • Illustrative QbD example: Transdermal drug delivery

Section 8 – Screening Components

  • Simplex: Gasoline additives
  • Non-simplex screening designs
    • Non-simplex screening exercise
      • Follow-up study
 Day 3  Section 1 – Combining Mixture and Process Variables
  •  Combined designs
    • Fish patties (user defined)
    • Fish patties (optimal)
   Section 2 – 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 3 – Mixture Amount & Mixtures with Categoric Factors
  • Mixture amount experiment: Ibuprofen
  • Mixture with categoric factors: Composite material
  • Categoric factors with proportion going to zero: Shelf life
   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 – Using Ratios of Components
  • Ratios as a natural scale: Gasoline blending
    • Using log ratios: Polymer formulation
  • Using ratios to combine designs
    • Combining mixtures: Three-layer film
    • Combining mixture and process: Reverse-phase HPLC 
   Section 6 – Special Topics (optional material as time allows)
  • Augmenting a mixture design: Sparklers
  • Sizing to detect a difference: Paint
  • Partial Quadratic Mixture (PQM) models
    • Linear with subset of squared and cross product terms 
   Section 7 – Review Exercises (optional material as time allows)
  • Mixture with MLCs: Blue haze
  • Combined mixture and process variables: Corn dogs
  • Mixture-amount experiment: Hormones
  • An additional equality constraint: Coating 
   Section 8 – Appendix
  • DOE Support
  • Reference material
    • Piepel’s vs. Cox’s direction (details)
    • Quartic and special quartic models
    • Cox's mixture models
    • Slack variable models


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

  • Experiments with Mixtures, 3rd Edition by John Cornell
  • Experimental Design for Formulation by Wendell Smith
  • Design-Expert® software for experimental design

Purchase the recommended software at the time of registration to receive a 20% discount. Recommended texts may be purchased from your favorite bookseller.