Discrepancy for uniform design of experiments with mixtures

The uniform design is a kind of space filling design that is robust against the model specification. The uniform design has been widely applied to experiments with mixtures. In this paper, we propose a new discrepancy DM2-discrepancy as a new criterion to measure the uniformity of designs with mixtures. A computational formula of the new discrepancy, by the functional method, is also given. This property overcome the main disadvantage of the discrepancies proposed before.