Order of Addition in Orthogonally Blocked Mixture and Component-Amount Designs

TL;DR

This paper explores the impact of the order of addition of components in orthogonally blocked mixture experiments, proposing designs that estimate both mixture effects and addition order, with efficiency and prediction assessments.

Contribution

It introduces mixture designs that incorporate the order of component addition in orthogonal blocks, addressing a gap in existing mixture experiment methodologies.

Findings

Designs enable estimation of order effects and mixture parameters.

G-efficiency measures design quality for parameter estimation.

Fraction of the Design Space plot visualizes prediction capabilities.

Abstract

Mixture experiments often involve process variables, such as different chemical reactors in a laboratory or varying mixing speeds in a production line. Organizing the runs in orthogonal blocks allows the mixture model to be fitted independently of the process effects, ensuring clearer insights into the role of each mixture component. Current literature on mixture designs in orthogonal blocks ignores the order of addition of mixture components in mixture blends. This paper considers the order of addition of components in mixture and mixture-amount experiments, using the variable total amount taken into orthogonal blocks. The response depends on both the mixture proportions or the amounts of the components and the order of their addition. Mixture designs in orthogonal blocks are constructed to enable the estimation of mixture or component-amount model parameters and the order-of-addition effects. The G-efficiency criterion is used to assess how well the design supports precise and unbiased estimation of the model parameters. The fraction of the Design Space plot is used to provide a visual assessment of the prediction capabilities of a design across the entire design space.