Design of Experiments for Mixtures

Compare factorial designs with mixture designs by emphasizing ingredient proportions that sum to one. Learn how mixture designs use squares and triangles to represent component fractions.

Learn how triangular plots represent three-component mixtures, with vertices as pure components, sides as binary blends, and interior points as three-component blends. Read fractions and ISO concentration lines.

Explore simplex designs for mixture experiments, including simplex lattice and simplex centroid designs, to study how component proportions affect the response under the constraint that proportions sum to one.

Explore simplex centroid designs as an alternative to lattice designs for mixture experiments, using permutations of one, halves, and thirds to generate seven or fifteen treatments with all components present.

Apply Schaeffer's linear model for three-component mixtures, using x1+x2+x3=1 to derive beta star, then expand to quadratic and cubic models with interaction terms and simplex lattice designs.

Learn to build simplex centroid and simplex lattice designs in R with the mix X package, for three and four components, including viewing ternary diagrams and exporting as csv.

Learn to solve and interpret a three-component mixture design using the simplex centroid approach to optimize sensory appeal and ascorbic acid in a mixed berry juice with coconut water.

Load the mix X library, import the data, and analyze mixture designs in R by comparing linear, quadratic, special cubic, and custom models for overall liking and ascorbic acid.

Select the best regression model using adjusted R squared and p-values, validate residuals with fitted values and Q-q plots, then build the final model and a contour plot.

Create a triangular contour plot for mixtures to reveal that pure strawberry or raspberry yields the highest liking, while blackberry lowers the response, showing antagonistic interaction between strawberry and raspberry.

Explore simplex lattice and simplex centroid designs as boundary point designs and augment them with interior Excel runs to improve mixture predictions, illustrated with a case study.

Analyze drug formulation using water, diclofenac, and atorvastatin to inhibit Acanthamoeba and assess eukaryotic toxicity, via a ten-point augmented simplex centric design with pure, binary, and ternary blends.

Analyze a three-component mixture with a special cubic model to predict Acanthamoeba growth. Identify significant interactions and note that binary mixtures with about 20% atorvastatin best inhibit growth.

We analyze four-component mixtures using ternary plots to optimize a flavonoid-rich food formulation (dates, raisins, pomegranates, figs) with a 20-run x-y design and centroid replicates for spatial cubic model analysis.

Analyze a four-component mixture design for total flavonoid content using a special cubic model; dates, raisins, and pomegranates drive content, figs reduce it.

Explore constrained mixture designs with a simplex centroid design inside a triangle, enforcing a minimum diesel of 0.8. Relate pseudo components to real concentrations for diesel, biodiesel, and ethanol.

Explore a constraint mixture design to develop an omega-3 oil nanoemulsion for improved drug delivery, focusing on globule size, drug loading, in vitro release, and mucosal penetration.

Build a constrained simplex lattice A[3,3] design in R with the mix X library and SLD function, compute real component concentrations from lower limits, and plot and export the design.

Analyze a simplex lattice A[3,3] design with constraints, fit cubic and quadratic models for globule size and drug loading, and identify mix: 10% omega-3, 30% HCO 40, 60% LA 21.

Introduce constrained designs for mixtures with an irregular region bounded by x1, x2, x3; build designs from extreme vertices and edge centroids, plus a facet centroid, using R code.

Build a constrained three-component surface design with vertex points, edge centroids, and the overall centroid, expand to an eleven-run cubic design via the opt Federov function, and save as csv.

Analyze constrained designs for peanut polvoron with a special cubic model in R, revealing sugar, peanut, and butter effects and interactions to optimize overall liking within a ternary region.