Order-of-addition in mixture and component-amount designs in orthogonal blocks.

Area of Science:

• * Experimental Design
• * Chemical Engineering
• * Pharmaceutical Sciences

Background:

• * Traditional mixture experiments focus on component proportions, often overlooking the impact of addition sequence.
• * Orthogonal block designs are crucial for independently estimating mixture and process variable parameters.
• * Order-of-addition (OofA) effects can significantly influence experimental responses but are often unaddressed.

Purpose of the Study:

• * To introduce and extend the concept of OofA effects within orthogonal block designs for mixture experiments.
• * To develop efficient designs for both mixture and component-amount experiments that incorporate OofA effects.
• * To enable the estimation of OofA effects and their interactions without confounding with block effects.

Main Methods:

• * Construction of mixture and component-amount designs in non-orthogonal blocks with pairwise ordering variables.
• * Application of the Threshold Accepting (TA) algorithm to generate G-optimal orthogonal designs in two blocks.
• * Development of designs allowing independent estimation of primary parameters and their interactions with OofA effects.

Main Results:

• * Proposed designs effectively incorporate OofA effects into mixture and component-amount experiments within orthogonal blocks.
• * The Threshold Accepting algorithm successfully reduced experimental runs while maintaining design efficiency.
• * Demonstrated ability to estimate mixture/component-amount parameters and their interactions with OofA effects, free from block confounding.

Conclusions:

• * Orthogonally blocked OofA designs offer a more comprehensive understanding of mixture and component-amount systems.
• * The methodology is particularly valuable for biomedical and pharmaceutical research where precise control over component addition is critical.
• * This approach enhances the efficiency and accuracy of experimental design in complex mixture systems.