Mixed-Level Column Augmented Uniform Designs
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In follow-up designs, some additional factors with two or three levels may be added in the follow-up stage since they are quite important but neglected in the first stage. Such follow-up designs are called mixed-level column augmented designs. In this paper, based on the initial designs, mixed-level column augmented uniform designs are proposed by using the uniformity criterion such as wrap-around L2-discrepancy (WD). The additional factors can be three-level or blocking, where the additional blocking factors can be regarded as additional common two-level factors. The multi-stage augmented situation is also investigated. We present the analytical expressions and the corresponding lower bounds of the WD of the column augmented designs. It is interesting to show that the column augmented uniform designs are also the optimal designs under the non-orthogonality criterion, E(f_NOD). Furthermore, a construction algorithm for the column augmented uniform design is provided. Some examples show that the lower bounds are tight and the construction algorithm is effective.
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