  Follow-up experimental designs are popularly used in industry. In many
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 may be
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, wrap-around $L_2$-discrepancy (WD). The multi-stage
augmented procedure which adds the additional design points stage by stage is
also investigated. We present the analytical expressions and the corresponding
lower bounds of 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, $E(f_{NOD})$. 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.
