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Alias Structures and Sequential Experimentation for Mixed-Level Designs

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  • Armando Javier Ríos-Lira

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

  • Yaquelin Verenice Pantoja-Pacheco

    (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

Alias structures for two-level fractional designs are commonly used to describe the correlations between different terms. The concept of alias structures can be extended to other types of designs such as fractional mixed-level designs. This paper proposes an algorithm that uses the Pearson’s correlation coefficient and the correlation matrix to construct alias structures for these designs, which can help experimenters to more easily visualize which terms are correlated (or confounded) in the mixed-level fraction and constitute the basis for efficient sequential experimentation.

Suggested Citation

  • Armando Javier Ríos-Lira & Yaquelin Verenice Pantoja-Pacheco & José Antonio Vázquez-López & José Alfredo Jiménez-García & Martha Laura Asato-España & Moisés Tapia-Esquivias, 2021. "Alias Structures and Sequential Experimentation for Mixed-Level Designs," Mathematics, MDPI, vol. 9(23), pages 1-21, November.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:23:p:3053-:d:689842
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    References listed on IDEAS

    as
    1. Kai-Tai Fang & Dennis K. J. Lin & Min-Qian Liu, 2003. "Optimal mixed-level supersaturated design," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 58(3), pages 279-291, December.
    2. DeCock, Dean & Stufken, John, 2000. "On finding mixed orthogonal arrays of strength 2 with many 2-level factors," Statistics & Probability Letters, Elsevier, vol. 50(4), pages 383-388, December.
    3. Yamada, Shu & Lin, Dennis K. J., 1999. "Three-level supersaturated designs," Statistics & Probability Letters, Elsevier, vol. 45(1), pages 31-39, October.
    4. Murat Kulahci & Søren Bisgaard, 2006. "A generalization of the alias matrix," Journal of Applied Statistics, Taylor & Francis Journals, vol. 33(4), pages 387-395.
    5. Koukouvinos, C. & Mantas, P., 2005. "Construction of some E(fNOD) optimal mixed-level supersaturated designs," Statistics & Probability Letters, Elsevier, vol. 74(4), pages 312-321, October.
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