Uniformity of Asymmetric Augmented Designs

Follow-up experimental designs are widely applied to explore the relationship between factors and responses step by step in various fields such as science and engineering.When some additional resources or information become available after the initial design of experiment is carried out,some additional runs and/or factors may be added in the follow-up stage.In this paper,the issue of the uniform row augmented designs and column augmented designs with mixed two-,three-and four-level is investigated.The uniformity of augmented designs is discussed under the wrap-around L_(2)-discrepancy.Some lower bounds of wrap-around L_(2)-discrepancy for the augmented designs are obtained,which can be used to assess uniformity of augmented design.Numerical results show that augmented designs have high efficiency,which have low discrepancy and close to the proposed lower bounds.

Designing Optimal Large Four-Level Experiments:A New TechniqueWithout Recourse to Optimization Softwares

Experimental design is an effective statistical tool that is extensively applied in modern industry,engineering,and science.It is proved that experimental design is a powerful and efficient means to screen the relationships between input factors and their responses,and to distinguish significant and unimportant factor effects.In many practical situations,experimenters are faced with large experiments having four-level factors.Even though there are several techniques provided to design such experiments,the challenge faced by the experimenters is still daunting.The practice has demonstrated that the existing techniques are highly time-consuming optimization procedures,satisfactory outcomes are not guaranteed,and non-mathematicians face a significant challenge in dealing with them.A new technique that can overcome these defects of the existing techniques is presented in this paper.The results demonstrated that the proposed technique outperformed the current techniques in terms of construction simplicity,computational efficiency and achieving satisfactory results capability.For non-mathematician experimenters,the new technique is much easier and simpler than the current techniques,as it allows them to design optimal large experiments without the recourse to optimization softwares.The optimality is discussed from four basic perspectives:maximizing the dissimilarity among experimental runs,maximizing the number of independent factors,minimizing the confounding among factors,and filling the experimental domain uniformly with as few gaps as possible.