Two-level parallel flats designs
The Annals of Statistics · 2021 · Volume 49 · Issue 5
Abstract
Regular 2n−p designs are also known as single flat designs. Parallel flats designs (PFDs) consisting of three parallel flats (3-PFDs) are the most frequently utilized PFDs, due to their simple structure. Generalizing to f-PFD with f>3 is more challenging. This paper aims to study the general theory for the f-PFD for any f≥3. We propose a method for obtaining the confounding frequency vectors for all nonequivalent f-PFDs, and to find the least G-aberration (or highest D-efficiency) f-PFD constructed from any single flat. PFDs are particularly useful for constructing nonregular fraction, split-plot or randomized block designs. We also characterize the quaternary code design series as PFDs. Finally, we show how designs constructed by concatenating regular fractions from different families may also have a parallel flats structure. Examples are given throughout to illustrate the results.
Keywords
62K05, 62K15, Confounding frequency vector, equivalent design, G-aberration, nonregular fractional factorial design, quaternary code, Sylvester Hadamard matrix, two-factor interaction model
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