Lower bounds of the average mixture discrepancy for row augmented designs with mixed four- and five-level

Follow-up experimental designs are widely used in various scientific investigations and industrial applications to discuss the relationship between inputs and outputs at various stages. Due to the limitation of run size, the desired experimental purpose may not be achieved through one stage of the experiment, so additional runs should be considered in the follow-up stage. By taking all possible level permutation of the factors into consideration, the uniformity of row augmented designs with mixed four- and five-level is discussed under the average mixture discrepancy, and new lower bounds of average mixture discrepancy for row augmented designs with mixed four- and five-level are obtained in this paper. Accordingly, the algorithm for the construction of uniform row augmented designs with mixed four- and five-level is proposed. Numerical examples show that the constructed uniform row augmented designs with mixed four- and five-level are highly efficient and can be used in practice.