@article{Ling2022, 
author = {Ling Ling and Guanghui Li and Xiaoyuan Zhu and Chongqi Zhang},
title = {R-optimal designs for second-order Scheffé model with qualitative factors},
year = {2022},
journal = {AIMS Mathematics},
volume = {7},
number = {3},
pages = {4540-4551},
keywords = {mixture experiments, qualitative factors, R-optimality, equivalence theorem},
url = {https://www.sciopen.com/article/10.3934/math.2022253},
doi = {10.3934/math.2022253},
abstract = {Considering a mixture model with qualitative factors, the    R-optimal design problem is investigated when the levels of the qualitative factor interact with the mixture factors. In this paper, the conditions for    R-optimality of designs with mixture and qualitative factors are presented. General analytical expressions are also derived for the decision function under the    R-optimal designs, in order to verify that the resulting designs satisfy the general equivalence theorem. In addition, the relative efficiency of the    R-optimal design is discussed.}
}