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Confidence sets for optimal factor levels of a response surface

Author

Listed:
  • Fang Wan
  • Wei Liu
  • Frank Bretz
  • Yang Han

Abstract

Construction of confidence sets for the optimal factor levels is an important topic in response surfaces methodology. In Wan et al. (2015), an exact (1−α) confidence set has been provided for a maximum or minimum point (i.e., an optimal factor level) of a univariate polynomial function in a given interval. In this article, the method has been extended to construct an exact (1−α) confidence set for the optimal factor levels of response surfaces. The construction method is readily applied to many parametric and semiparametric regression models involving a quadratic function. A conservative confidence set has been provided as an intermediate step in the construction of the exact confidence set. Two examples are given to illustrate the application of the confidence sets. The comparison between confidence sets indicates that our exact confidence set is better than the only other confidence set available in the statistical literature that guarantees the (1−α) confidence level.

Suggested Citation

  • Fang Wan & Wei Liu & Frank Bretz & Yang Han, 2016. "Confidence sets for optimal factor levels of a response surface," Biometrics, The International Biometric Society, vol. 72(4), pages 1285-1293, December.
    • Handle: RePEc:bla:biomet:v:72:y:2016:i:4:p:1285-1293
    DOI: 10.1111/biom.12500
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    References listed on IDEAS

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    1. Del Castillo E. & Cahya S., 2001. "A Tool for Computing Confidence Regions on the Stationary Point of a Response Surface," The American Statistician, American Statistical Association, vol. 55, pages 358-365, November.
    2. John J. Peterson & Suntara Cahya & Enrique Castillo, 2002. "A General Approach to Confidence Regions for Optimal Factor Levels of Response Surfaces," Biometrics, The International Biometric Society, vol. 58(2), pages 422-431, June.
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    Cited by:

    1. Gianluca Trotta & Stefania Cacace & Quirico Semeraro, 2022. "Process optimization via confidence region: a case study from micro-injection molding," Journal of Intelligent Manufacturing, Springer, vol. 33(7), pages 2045-2057, October.
    2. Zhou, Sanyu & Wan, Fang & Liu, Wei & Bretz, Frank, 2017. "Computation of an exact confidence set for a maximum point of a univariate polynomial function in a given interval," Statistics & Probability Letters, Elsevier, vol. 122(C), pages 157-161.
    3. Wei Liu & Frank Bretz & Natchalee Srimaneekarn & Jianan Peng & Anthony J. Hayter, 2019. "Confidence Sets for Statistical Classification," Stats, MDPI, vol. 2(3), pages 1-15, June.

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    1. Gianluca Trotta & Stefania Cacace & Quirico Semeraro, 2022. "Process optimization via confidence region: a case study from micro-injection molding," Journal of Intelligent Manufacturing, Springer, vol. 33(7), pages 2045-2057, October.

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