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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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to study the issue of employing the uniformity criterion measured by the mixture discrepancy to assess the optimal foldover plans for q-level factorials. The average mixture discrepancy and the average projection mixture discrepancy based on the level permutation method are respectively defined for combined designs, and the optimal foldover plan in terms of the overall uniformity and the uniformity of each dimension are also explored. The tight lower bounds of the average mixture discrepancy and the uniformity pattern under the general foldover plan are obtained respectively, which can be used as a benchmark for searching optimal foldover plans. Some illustrative examples are provided to show the theoretical results. [ABSTRACT FROM AUTHOR]

The issue of the projection uniformity of mixed two- and three-level factorials measured by mixture discrepancy is investigated in this paper. The average projection mixture discrepancy is defined to measure the uniformity for low-dimensions projection designs. Moreover, the relationship between uniformity pattern and generalized minimum aberration is established. Two numerical examples are provided to illustrate the theoretical results. [ABSTRACT FROM AUTHOR]

Follow-up experiment is widely applied to various fields such as science and engineering, since it is an indispensable strategy, especially when some additional resources or information become available after the initial design of experiment is carried out. Moreover, some extra factors may be added in the follow-up experiment. One may augment the number of runs and/or factors for the purpose of application. In this paper, the issue of the uniform row augmented designs and column augmented designs with mixed two- and three-level is investigated. The uniformity of augmented designs is discussed under the Lee discrepancy, some lower bounds of Lee discrepancy for the augmented designs are obtained. The construction algorithm of the uniform augmented designs is given. Some numerical examples indicate that uniform augmented designs can be constructed with high efficiency. [ABSTRACT FROM AUTHOR]