IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v9y2021i23p3053-d689842.html
   My bibliography  Save this article

Alias Structures and Sequential Experimentation for Mixed-Level Designs

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/9/23/3053/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/9/23/3053/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Yamada, Shu & Lin, Dennis K. J., 1999. "Three-level supersaturated designs," Statistics & Probability Letters, Elsevier, vol. 45(1), pages 31-39, October.
    2. 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.
    3. 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.
    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Chen, Jie & Liu, Min-Qian, 2008. "Optimal mixed-level supersaturated design with general number of runs," Statistics & Probability Letters, Elsevier, vol. 78(15), pages 2496-2502, October.
    2. Gupta, V.K. & Singh, Poonam & Kole, Basudev & Parsad, Rajender, 2009. "Construction of efficient unbalanced mixed-level supersaturated designs," Statistics & Probability Letters, Elsevier, vol. 79(22), pages 2359-2366, November.
    3. Koukouvinos, C. & Stylianou, S., 2004. "Optimal multi-level supersaturated designs constructed from linear and quadratic functions," Statistics & Probability Letters, Elsevier, vol. 69(2), pages 199-211, August.
    4. 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.
    5. Chasiotis, Vasilis & Kounias, Stratis & Farmakis, Nikolaos, 2017. "Upper bound on the number of multi-level columns in equally replicated optimal designs minimizing the E(fNOD) criterion," Statistics & Probability Letters, Elsevier, vol. 129(C), pages 269-274.
    6. Liu, Min-Qian & Zhang, Li, 2009. "An algorithm for constructing mixed-level k-circulant supersaturated designs," Computational Statistics & Data Analysis, Elsevier, vol. 53(7), pages 2465-2470, May.
    7. Li, Peng-Fei & Liu, Min-Qian & Zhang, Run-Chu, 2004. "Some theory and the construction of mixed-level supersaturated designs," Statistics & Probability Letters, Elsevier, vol. 69(1), pages 105-116, August.
    8. Mandal, B.N. & Koukouvinos, C., 2014. "Optimal multi-level supersaturated designs through integer programming," Statistics & Probability Letters, Elsevier, vol. 84(C), pages 183-191.
    9. Yan Liu & Min-Qian Liu, 2012. "Construction of equidistant and weak equidistant supersaturated designs," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 75(1), pages 33-53, January.
    10. Li, Hongyi & Qin, Hong, 2018. "Some new results on Triple designs," Statistics & Probability Letters, Elsevier, vol. 139(C), pages 1-9.
    11. Chatterjee, Kashinath & Qin, Hong, 2008. "A new look at discrete discrepancy," Statistics & Probability Letters, Elsevier, vol. 78(17), pages 2988-2991, December.
    12. Hong Qin & Na Zou & Kashinath Chatterjee, 2009. "Connection between uniformity and minimum moment aberration," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 70(1), pages 79-88, June.
    13. Pang, Shanqi & Zhang, Yingshan & Liu, Sanyang, 2004. "Further results on the orthogonal arrays obtained by generalized Hadamard product," Statistics & Probability Letters, Elsevier, vol. 68(1), pages 17-25, June.
    14. Nguyen, Nam-Ky & Liu, Min-Qian, 2008. "An algorithmic approach to constructing mixed-level orthogonal and near-orthogonal arrays," Computational Statistics & Data Analysis, Elsevier, vol. 52(12), pages 5269-5276, August.
    15. Zhou, Yong-Dao & Ning, Jian-Hui & Song, Xie-Bing, 2008. "Lee discrepancy and its applications in experimental designs," Statistics & Probability Letters, Elsevier, vol. 78(13), pages 1933-1942, September.
    16. 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.
    17. Yang, Xue & Chen, Hao & Liu, Min-Qian, 2014. "Resolvable orthogonal array-based uniform sliced Latin hypercube designs," Statistics & Probability Letters, Elsevier, vol. 93(C), pages 108-115.
    18. Rong-Xian Yue & Kashinath Chatterjee, 2010. "Bayesian U-type design for nonparametric response surface prediction," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 72(2), pages 219-231, September.
    19. S. Georgiou & C. Koukouvinos, 2006. "Multi-level k-circulant Supersaturated Designs," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 64(2), pages 209-220, October.
    20. Georgiou, S. & Koukouvinos, C. & Mantas, P., 2003. "Construction methods for three-level supersaturated designs based on weighing matrices," Statistics & Probability Letters, Elsevier, vol. 63(4), pages 339-352, July.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:9:y:2021:i:23:p:3053-:d:689842. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.