Projective properties of certain orthogonal arrays

Unknown author

113 citations0/0 files storedBiometrika

No readable copy stored yet — this record is metadata only.

No open-access location is known for this record yet.

Literature note Cite in a project Citation map

Optimal Experimental Design Methods Advanced Combinatorial Mathematics Statistical Methods and Applications

Abstract

A question of importance in factor screening is when a two-level orthogonal design for a multifactor experiment can be projected into lower dimension, typically P = 2 or 3. New results relate to the projectivity P of saturated designs in which n − 1 factors are tested in n runs. It is shown that: a design obtained by ‘doubling’ an n × n orthogonal array is always of projectivity P = 2; a two-level cyclic design is either a factorial array, and hence has P = 2, or it has P = 3; a two-level orthogonal design with 4m runs, m odd, has P = 3. In particular these results allow the designs derived by Plackett & Burman (1946) to be categorised in terms of these projective properties.

Paper brief

Loading…

Cite this work

Citation unavailable for this work.

BibTeX RIS CSL-JSON

No public copy is stored for this record, so only the metadata is cited.

Citations in this library

Citation map →

Stored only when both papers are in the corpus — 113 citations exist upstream.

References

1946THE DESIGN OF OPTIMUM MULTIFACTORIAL EXPERIMENTS 1992On the Experimental Attainment of Optimum Conditions 1986An Analysis for Unreplicated Fractional Factorials 1973Constructions and Combinatorial Problems in Design of Experiments 1947Factorial Experiments Derivable from Combinatorial Arrangements of Arrays 2000The 2 k-p Fractional Factorial Designs Part I 1943THE FRACTIONAL REPLICATION OF FACTORIAL ARRANGEMENTS 1986Dispersion Effects from Fractional Designs

Cited by

1996Follow-Up Designs to Resolve Confounding in Multifactor Experiments 2009Recent developments in nonregular fractional factorial designs 2001Theory of J-characteristics for fractional factorial designs and projection justification of minimum G2-aberration 2001One hundred years of the design of experiments on and off the pages of Biometrika 2004k-Circulant Supersaturated Designs 2018R Package DoE.base for Factorial Experiments

Explore the map →

Papers that cite the same references — the relational fallback while embeddings are still backfilling.

Imported from OpenAlex (CC0) — nothing here is generated.