Some new results on Triple designs

The method of doubling has been used to construct two-level fractional factorial designs. Zhang (2016) extended the method of doubling to the method of tripling, which has been used to construct three-level fractional factorial designs. Various popular screening criteria, such as E(fNOD) criterion, generalized minimum aberration (GMA), minimum moment aberration (MMA), B criterion and uniformity criterion, have been proposed from different viewpoints to compare and construct designs. In this paper, the analytic connections between Triple designs constructed by tripling and initial designs under the above screening criteria are considered. These connections are suitable to general original three-level fractional factorial designs, whether regular or nonregular. Furthermore, the connections provide theoretical basis for constructing a kind of optimal three-level designs with large sizes by tripling successively.