Construction of Saturated D-optimal Designs for Mixture Experiments with a Non Normal Response using an Algorithmic Search

Background: Mixture experiments belong to the response surface design category, involving the combination of multiple components to create a product. These products are commonly encountered in daily life. In some cases, mixture experiments yield qualitative responses, such as taste in a fruit punch. Qualitative variables often deviate from a normal distribution. 

Methods: To address non-normal responses, a generalized linear model, specifically the logistic model, is employed. This study utilizes logistic models and develops suitable search algorithms to obtain saturated D-optimal designs for mixture experiments. The validation of D-optimality criteria is based on the General Equivalence Theorem. 

Result: For generating locally D-optimal designs, the logistic model is utilized considering non-normally distributed errors. While the procedure remains the same for other nonlinear models, the assumptions regarding error distribution impact the Fisher information matrix (FIM).