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A Numerical Stability Analysis in the Inclusion of an Inverse Term in the Design of Experiments for Mixtures

Author

Listed:
  • Javier Cruz-Salgado

    (School of Engineering, Industrial Engineering and Mechanical Engineering Department, Universidad de las Américas Puebla (UDLAP), Puebla 72810, Mexico)

  • Sergio Alonso-Romero

    (Centro de Innovación Aplicada en Tecnologías Competitivas CIATEC, Biomecánica, León 37545, Mexico)

  • Edgar Augusto Ruelas-Santoyo

    (Department of Industrial Engineering, Instituto Tecnológico de Celaya, Celaya 38010, Mexico)

  • Israel Miguel-Andrés

    (Centro de Innovación Aplicada en Tecnologías Competitivas CIATEC, Biomecánica, León 37545, Mexico)

  • Roxana Zaricell Bautista-López

    (Centro de Innovación Aplicada en Tecnologías Competitivas CIATEC, Biomecánica, León 37545, Mexico)

  • Amir Hossein Nobil

    (Escuela de Ingeniería y Ciencias, Tecnologico de Monterrey, Ave. Eugenio Garza Sada 2501, Monterrey 64849, Mexico)

Abstract

A mixture experiment is one where the response depends only on the relative proportions of the ingredients present in the mixture. Different regression models are used to analyze mixture experiments, such as the Scheffé model, the Slack Variable model, and models with inverse terms. Models with inverse terms are worthy of consideration in certain applications. These models have been analyzed considering their fit quality, but not their numerical stability. This article analyzes the numerical stability of the model with inverse terms and the use of pseudo components. Likewise, a criterion is defined for the selection of the regression model with inverse terms, based on the quality of fit and numerical stability.

Suggested Citation

  • Javier Cruz-Salgado & Sergio Alonso-Romero & Edgar Augusto Ruelas-Santoyo & Israel Miguel-Andrés & Roxana Zaricell Bautista-López & Amir Hossein Nobil, 2024. "A Numerical Stability Analysis in the Inclusion of an Inverse Term in the Design of Experiments for Mixtures," Mathematics, MDPI, vol. 12(22), pages 1-11, November.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:22:p:3587-:d:1522167
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    References listed on IDEAS

    as
    1. Andre Khuri, 2005. "Slack-variable models versus Scheffe's mixture models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 32(9), pages 887-908.
    2. M. Cain & M. L. R. Price, 1986. "Optimal Mixture Choice," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 35(1), pages 1-7, March.
    3. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
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