A lower bound of average mixture discrepancy for row augmented designs

Follow-up experimental designs are frequently employed in a wide range of scientific studies and industries. Lower bounds of average mixture discrepancy for row augmented designs are determined in this paper utilizing the level permutation technique, which is also used to analyse the uniformity of row augmented designs with asymmetrical factorials. Between the row augmented designs and its initial designs or follow-up designs, quantitative relationships of lower bounds of average mixture discrepancy are constructed. Additionally, a proposal is made for the construction algorithm of asymmetrical uniform row augmented designs. Numerical examples indicate that the asymmetrical uniform row augmented designs can be constructed with high efficiency and recommended for use in practice.