Weighted R-efficiency optimal design for experiments with mixture

Abstract

In this paper, we proposed a weighted R-efficiency optimal design (WROD) criterion to obtain an effective design for experiments with the mixture when the assumed model is unknown. our approach is via maximizing weighted R-efficiency for the set of candidate models to achieve. Moreover, we discussed the WROD for Kronecker models with first- and second-order and obtained some results. (i) The equivalence theorem for the WROD is proved; (ii) The WROD has higher efficiency than R-optimal design; (iii) Flexibility in assumptions about the model, and more robust; (iv) The efficiency values of the WROD for different prior distributions were obtained by simulation.