Table of Contents
- 1 Optimal Tools for Formulation Development
- 1.1 Building a simplex-lattice design
- 1.2 Analyzing a mixture design
- 1.3 Basics of numerical optimization
- 1.4 Using optimal designs for constraints
- 1.5 Using data transformations to improve predictions
- 1.6 Adding cost equations
- 1.7 Optimal designs for multi-component constraints
- 1.8 Group constraints
- 1.9 Ratio constraints
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.
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
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.
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