One Note for Fractionation and Increase for Mixed-Level Designs When the Levels Are Not Multiple

Yaquelin Verenice Pantoja-Pacheco, Armando Javier Ríos-Lira, José Antonio Vázquez-López, José Alfredo Jiménez-García, Martha Laura Asato-España and Moisés Tapia-Esquivias
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Yaquelin Verenice Pantoja-Pacheco: Tecnológico Nacional de México/Instituto Tecnológico de Celaya, Celaya 38010, Mexico
Armando Javier Ríos-Lira: Tecnológico Nacional de México/Instituto Tecnológico de Celaya, Celaya 38010, Mexico
José Antonio Vázquez-López: Tecnológico Nacional de México/Instituto Tecnológico de Celaya, Celaya 38010, Mexico
José Alfredo Jiménez-García: Tecnológico Nacional de México/Instituto Tecnológico de Celaya, Celaya 38010, Mexico
Martha Laura Asato-España: Tecnológico Nacional de México/Instituto Tecnológico de Celaya, Celaya 38010, Mexico
Moisés Tapia-Esquivias: Tecnológico Nacional de México/Instituto Tecnológico de Celaya, Celaya 38010, Mexico

Mathematics, 2021, vol. 9, issue 13, 1-20

Abstract: Mixed-level designs have a wide application in the fields of medicine, science, and agriculture, being very useful for experiments where there are both, quantitative, and qualitative factors. Traditional construction methods often make use of complex programing specialized software and powerful computer equipment. This article is focused on a subgroup of these designs in which none of the factor levels are multiples of each other, which we have called pure asymmetrical arrays. For this subgroup we present two algorithms of zero computational cost: the first with capacity to build fractions of a desired size; and the second, a strategy to increase these fractions with M additional new runs determined by the experimenter; this is an advantage over the folding methods presented in the literature in which at least half of the initial runs are required. In both algorithms, the constructed fractions are comparable to those showed in the literature as the best in terms of balance and orthogonality.

Keywords: mixed-level; balance; orthogonality (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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