Generalised minimum moment aberration for designs with both qualitative and quantitative factors

The minimum moment aberration and the minimum Lee‐moment aberration criteria are two popular conceptually simple and computationally cheap criteria for selecting good designs. However, the minimum moment aberration is suitable for qualitative factors, and the minimum Lee‐moment aberration cannot distinguish some designs with high‐level quantitative factors. In this paper, the minimum absolute‐moment aberration criterion is proposed to compare and select designs with multi‐level quantitative factors. We validate the statistical justifications of this criterion from theoretical and numerical aspects. Furthermore, we extend the minimum absolute‐moment aberration criterion into screening designs with both qualitative and quantitative factors, naming the new criterion as the minimum mixed‐moment aberration criterion. Then we utilise a numerical study to compare and evaluate the performance of some popular designs with both qualitative and quantitative factors in computer experiments.