Mixed-level column augmented uniform designs.

In many industrial applications, follow-up experimental designs are often used to explore the relationship between inputs (factors) and outputs (responses) step by step. Some extra factors with two or three levels may be added in the follow-up stage since they are quite important but may be neglected in the initial stage. In this paper, mixed-level column augmented uniform designs are proposed under the uniformity criterion, wrap-around L 2 -discrepancy (WD). The multi-stage augmented procedure is also investigated. We present the analytical expressions and the corresponding lower bounds on the WD of the column augmented designs. It is shown that the column augmented uniform designs are also the optimal designs under the non-orthogonality criterion, E (f N O D). Furthermore, a construction algorithm for column augmented uniform designs is provided. Some examples show that the lower bounds are tight and the construction algorithm is effective. [ABSTRACT FROM AUTHOR]