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Use of indicator functions to enumerate cross-array designs without direct product structure

Satoshi Aoki and Masayuki Noro

Vol. 14 (2023), No. 2, 167–179

Use of polynomial indicator functions to enumerate fractional factorial designs with given properties was first introduced by Fontana, Pistone and Rogantin (2000) for two-level factors, and generalized by Aoki (2019) for multilevel factors. We apply this theory to enumerate cross-array designs. For experiments with several control factors and noise factors, use of the cross-array designs with direct product structure is widespread as an effective robust strategy in the Taguchi method. We relax this direct product structure to reduce the size of the designs. We obtain 24-runs cross-array designs without direct product structure with some desirable properties for six control factors and three noise factors, each with two levels, instead of the 32-runs design that is widely used.

computational algebraic statistics, cross-array designs, fractional factorial designs, Gröbner bases, indicator functions, Taguchi methods
Mathematical Subject Classification
Primary: 13P10, 62K15, 62R01
Received: 28 September 2022
Revised: 4 June 2023
Accepted: 11 July 2023
Published: 16 May 2024
Satoshi Aoki
Graduate School of Science
Faculty of Science
Kobe University
Masayuki Noro
Department of Mathematics
College of Science
Rikkyo University