Optimal Tools for Formulation Development

Optimal Tools for Formulation Development

When engaged in product formulation, conventional factorial designs prove inadequate; optimal experimentation necessitates the utilization of mixture designs. Contact us for the Design Expert training on Formulation Development.

During this Optimal Tools for Formulation Development short course you will:

  • Explore the characteristics of mixture experiments
  • Arrange simplex designs
  • Choose fitting mixture models
  • Generate contemporary visuals depicting design space
  • Apply optimal designs for restricted mixture variables
  • Enhance product formulations through optimization.


  • Knowledge of basic statistics (mean and standard deviation)
  • Exposure to simple comparative experiments (e.g. two-sample t-test) are recommended.
Topics Included:

Building a simplex-lattice design

This design differs from a simplex-centroid design by having enough points to estimate a full cubic model.

  • Applicable for 2 to 30 components
  • Simplex-lattice design with degree m comprises m+1 equally spaced values (0 to 1) per component
  • Fractions range for m = 2: 0, 1/2, 1
  • Fractions range for m = 3: 0, 1/3, 2/3, 1
  • Includes pure components and intermediary points for degree m estimation

Analyzing a mixture design

The analysis of a mixture design is based on the same principle as linear regression.

  • Employ Analyze Mixture Design for designed experiment analysis
  • Suitable when response hinges on mixture component proportions, e.g., bread dough ingredients
  • Incorporate process variables and total mixture quantities in analysis

Basics of numerical optimization

Numerical optimization involves a hill climbing approach, aiming to locate optimal solutions within a given parameter space. Beyond the designated design points, this technique incorporates a validation process that examines a collection of random points.

  • Select factor and response goals from the menu
  • Goals include: maximize, minimize, target, within range, none (responses), set to exact value (factors)
  • Each parameter needs minimum and maximum levels
  • Assign weights to goals for adjusting desirability function shape
  • Adjust goal importance relative to other goals.

Using optimal designs for constraints

This tutorial explains how Design Expert software constructs a response surface method (RSM) experiment within a non-uniform process space..

  • Employing specialized experimental designs
  • Addressing limitations or restrictions on mixture components
  • Optimizing designs to accommodate specific constraints
  • Enhancing efficiency and effectiveness of experimentation.

Using data transformations to improve predictions

It involves applying mathematical functions to the data to achieve more accurate and meaningful predictions:

  • Applying mathematical functions to data
  • Enhancing accuracy and meaning of predictions
  • Beneficial for non-linear or intricate scenarios
  • Uncovering hidden patterns and relationships for better insights.

Adding cost equations

Adding cost equations refers to incorporating mathematical expressions that quantify the costs associated with different experimental factors and conditions..

  • Including equations representing associated costs
  • Relevant for balancing response optimization and cost minimization
  • Customizing experimental designs for efficient resource utilization.

Optimal designs for multi-component constraints

Optimal designs are necessary when there are unequal component ranges, multi-component constraints, or a custom model is being fit to the responses.

  • Optimal designs offer enhanced flexibility
  • Unlike simplex designs, optimal designs use an algorithmic point selection approach
  • Points are chosen to achieve specific properties
  • Multiple statistically equivalent sets of design points often exist
  • This can lead to slight design variations for the same factors and model information

Group constraints

Instead of considering individual factors independently, group constraints impose conditions on combinations of factors.

  • Constraints involving multiple factors simultaneously
  • Addressing relationships and interactions between factors
  • Important for achieving complex experimental objectives.

Ratio constraints

These constraints are utilized when the relationships between factors are better represented through their ratios rather than their absolute values.

  • Constraints on ratios between variables or factors
  • Useful for representing relationships through ratios
  • Enhancing accuracy in complex experimental scenarios

Design Expert Training on Optimal Tools for Formulation Development