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

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  • Yaquelin Verenice Pantoja-Pacheco

    (Tecnológico Nacional de México/Instituto Tecnológico de Celaya, Celaya 38010, Mexico
    Tecnológico Nacional de México/Instituto Tecnológico de Celaya, Dpto. de Ingeniería Industrial, Antonio García Cubas No. 600, CP 38010, Fovissste, Celaya, Guanajuato, México.)

  • 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)

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.

Suggested Citation

  • Yaquelin Verenice Pantoja-Pacheco & Armando Javier Ríos-Lira & José Antonio Vázquez-López & José Alfredo Jiménez-García & Martha Laura Asato-España & Moisés Tapia-Esquivias, 2021. "One Note for Fractionation and Increase for Mixed-Level Designs When the Levels Are Not Multiple," Mathematics, MDPI, vol. 9(13), pages 1-20, June.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:13:p:1455-:d:579226
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    References listed on IDEAS

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