Abstract

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.

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