K‐Optimal Designs for an Additive Quadratic Mixture Model

ABSTRACT This article investigates K‐optimal designs for the additive quadratic model for mixture experiments. The primary aim of the K‐optimality criterion is to mitigate multicollinearity in regression analysis. It is demonstrated that the support points of K‐optimal designs, depending on the number of mixture components, include the vertices of the regular simplex along with the barycentres of depth one and two. The present study further illustrates that A‐optimal designs are more effective than D‐optimal designs in addressing multicollinearity issues. Notably, it is observed that the proposed K‐optimal designs also satisfy near dual‐optimality criteria, fulfilling both K‐optimality and A‐optimality.