D-optimal design of the additive mixture model with multi-response

Area of Science:

• Statistics
• Experimental Design

Background:

• Additive mixture models are widely used in various scientific fields.
• Designing experiments for these models requires efficient methods to optimize information gained.

Purpose of the Study:

• To propose a D-optimal design for additive mixture models with two response variables.
• To identify the conditions and weights that ensure D-optimality for these models.

Main Methods:

• The study employs the general equivalence theorem to validate the proposed design.
• Mathematical derivations are used to find the specific weights for D-optimality.

Main Results:

• A D-optimal design for the two-response additive mixture model is successfully proposed.
• The corresponding weights that satisfy D-optimality under the additive model are determined.

Conclusions:

• The proposed D-optimal design provides an efficient approach for experiments involving two-response additive mixture models.
• The findings offer practical guidance for researchers in selecting optimal experimental designs.