Near D-optimal designs

Since the optimal added points for the minimal-point design based on 2^k fractional factorial design with resolution III^* and Plackett and Burman design may not be useful in practice, we propose the near D-optimal designs by rounding optimal added supports.

1. Minimal-point composite design based on 2^k fractional factorial design with resolution III^*

four factors、six factors

1. Minimal-point composite design with Plackett and Burman Design

three factors、five factors、seven factors、eight factors

2. Comparison

We use relative efficiency to compare minimal-point design with near D-optimal designs, and the ratios are shown in the last column of Table 7.

Factor	Minimal-point design	Near D-optimal design	Relative efficiency
3	0.6680	0.6680 , 0.6611	1 , 0.9896
4	0.7115	0.7113	0.9997
5	0.7580	0.7561	0.9975
6	0.7810	0.7814	1.0005
7	0.6868	0.6808	0.9913
8	0.6278	0.6224 , 0.6220	0.9914 , 0.9908

Table 7. The P_eff values of minimal-point designs and near-optimal designs.