D-optimal designs in two orthogonal blocks for Darroch and Waller's quadratic model in constrained mixture components

摘要

Prescott and Draper (1998) obtained D-Optimal orthogonal block designs for Scheffe's quadratic model in case when one component is taken as filler and remaining components are constrained by upper bounds. In this paper, we obtain D-optimal orthogonal designs in two blocks for Darroch and Waller's quadratic models in three and four components, when many ingredients are included in small quantities and the main ingredient is used as a filler to make up the total of the mixture.