Table of Contents
Mixture Design for Optimal Formulations
When engaged in product formulation, conventional factorial designs are inadequate; optimal experimentation requires the application of mixture designs for enhanced efficacy. In scenarios where both formulation adjustments and product processing are integral, the most effective approach lies in adopting combined mixture-process designs. This immersive and interactive workshop equips you with the essential skills to proficiently navigate formulation studies, spanning the entire spectrum from screening to optimization. Contact us for the Design Expert training.
During the Mixture Design for Optimal Formulations workshop you will:
- Uncover the characteristics of a mixture experiment
- Arrange simplex designs
- Enhance and assess design quality
- Choose fitting mixture models
- Create contour plots within triangular space
- Develop designs considering constrained mixture variables
- Optimize product formulations
- Integrate mixture and process variables
- Enhance process comprehension through mixture-amount and mixture-categoric designs
- Knowledge of basic statistics (mean and standard deviation)
- Exposure to simple comparative experiments (e.g. two-sample t-test) are recommended
Introduction to Mixtures
Mixture models are easily interpretable only when all mixture components span from 0 to the total value within the design. However, many mixture designs encompass more restricted spaces.
- Mixture (Scheffé) polynomials: Scheffé models were uniquely formulated to effectively manage the inherent limitations present in mixture designs.
- Simplex-Lattice designs: 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
Constrained Mixtures, Simplex
A simplex design refers to a mixture design characterized by the systematic arrangement of design points on an L-simplex lattice.
Blocking a simplex design involves creating separate groups or blocks within the design to account for potential variability or external factors that could influence the results.
- Dividing the design into distinct blocks or groups
- Addresses potential sources of variability or external influences
- Enhances control over experimental conditions and results.
Constrained Mixtures, Non-Simplex
Non-simplex refers to experimental designs that do not adhere to the arrangement pattern of a simplex lattice. In other words, these designs involve design points that are not uniformly distributed on an L-simplex, deviating from the specific geometric structure characteristic of simplex designs.
Multicomponent Linear Constraints
Multiple Linear Constraints is a technique used to impose restrictions on the factors and responses in experimental designs.
- MLC Primer: MLC designs involve the integration of both mixture variables (related to ingredient proportions) and process variables (associated with manufacturing conditions) in experimental setups.
- 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
Screening designs cater to mixtures comprising 6 to 50 components. Beyond 24 components, it's necessary for the components to possess roughly equivalent ranges, ideally with minimal additional restrictions.
- Simplex: A simplex design refers to a mixture design characterized by the systematic arrangement of design points on an L-simplex lattice.
- Non-Simplex: Non-simplex refers to experimental designs that do not adhere to the arrangement pattern of a simplex lattice. In other words, these designs involve design points that are not uniformly distributed on an L-simplex, deviating from the specific geometric structure characteristic of simplex designs.
Combining Mixture and Process Variables
Design Expert software provides designs that incorporate both mixture components and process factors, whether they are numeric or categorical. In this tutorial, you'll explore the distinctive capabilities of Design Expert for designing and analyzing mixture-process experiments, focusing on the following investigations:
- Fish patties (background)
- Fish patties (optimal design)
Special Mixture and Process Problems
This refers to unique and challenging scenarios that involve both mixture components and process variables.
- Departure from typical experimental conditions
- Caused by intricate interactions, constraints, or particular formulation and processing objectives
- Necessitates inventive experimental design strategies
- Demands advanced analysis techniques
- Aims to attain optimal results in unique scenarios.
KCV model: The fundamental concept behind KCV designs involves initiating with an authentic second-order model for both mixture and process variables, followed by the application of the mixture constraint.