Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1149011 | Journal of Statistical Planning and Inference | 2014 | 6 Pages |
•We generalize the GMC theory into non regular designs.•For any given design, the G2-AENP is unique up to isomorphism.•Cores of criteria GMA and MMA are both functions on the G2-AENP.•The G2-GMC criterion is more powerful than GMA and MMA in the design recognition.•The G2-AENP is helpful for the arrangement of factors.
We extend the work of Zhang et al. [Statistica Sinica 18, 1689–1705] for nonregular designs and propose two new concepts, i.e., the generalized aliasing effect-number pattern (G2-AENP) and the generalized general minimum lower order confounding (G2-GMC). It proves that (i) isomorphic designs have the identical G2-AENP and (ii) the generalized minimum aberration (GMA) and minimum moment aberration (MMA) can both be treated as ones that optimize functions over the G2-AENP. That is, the G2-GMC criterion is more sensitive in the identification and classification of designs.