Construction on two-level factorials with flexible partially replicated runs via quarter foldover

•A technique is proposed to construct two-level factorials with flexible replicated runs.•Results show that the constructed designs are more flexible than the existing results.•A catalog of optimal designs with partially replicated runs is tabulated for practice.

Fractional factorial designs with partially replicated runs are desirable, since they not only save experimental cost and but also estimate the experimental error variance. In this paper, a simple technique called as quarter foldover, which can construct two-level factorial designs with flexible partially replicated runs, is firstly proposed. For an unreplicated initial design with resolution III (IV) or higher, whether regular or not, the sufficient and necessary conditions for the constructed design to be a resolution III (IV) or higher design with flexible partially replicated runs are investigated by the tool of indicator function. Theoretical results and examples show that the constructed designs are more flexible than most of the existing results in terms of the replicated runs. For initial designs of 12, 16, 20 and 24 runs with s factors, where 3≤s≤6, a catalog of optimal plans to construct some designs with highest resolution and flexible partially replicated runs is also tabulated for practice.