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A Bayesian Approach for Multiple Response Surface Optimization in the Presence of Noise Variables

Author

Listed:
  • Guillermo Miro-Quesada
  • Enrique Del Castillo
  • John Peterson

Abstract

An approach for the multiple response robust parameter design problem based on a methodology by Peterson (2000) is presented. The approach is Bayesian, and consists of maximizing the posterior predictive probability that the process satisfies a set of constraints on the responses. In order to find a solution robust to variation in the noise variables, the predictive density is integrated not only with respect to the response variables but also with respect to the assumed distribution of the noise variables. The maximization problem involves repeated Monte Carlo integrations, and two different methods to solve it are evaluated. A Matlab code was written that rapidly finds an optimal (robust) solution in case it exists. Two examples taken from the literature are used to illustrate the proposed method.

Suggested Citation

  • Guillermo Miro-Quesada & Enrique Del Castillo & John Peterson, 2004. "A Bayesian Approach for Multiple Response Surface Optimization in the Presence of Noise Variables," Journal of Applied Statistics, Taylor & Francis Journals, vol. 31(3), pages 251-270.
    • Handle: RePEc:taf:japsta:v:31:y:2004:i:3:p:251-270
    DOI: 10.1080/0266476042000184019
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    Citations

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    Cited by:

    1. Ouyang, Linhan & Ma, Yizhong & Wang, Jianjun & Tu, Yiliu, 2017. "A new loss function for multi-response optimization with model parameter uncertainty and implementation errors," European Journal of Operational Research, Elsevier, vol. 258(2), pages 552-563.
    2. Meng-Leong How & Yong Jiet Chan & Sin-Mei Cheah, 2020. "Predictive Insights for Improving the Resilience of Global Food Security Using Artificial Intelligence," Sustainability, MDPI, vol. 12(15), pages 1-14, August.
    3. Shun Matsuura, 2014. "Effectiveness of a random compound noise strategy for robust parameter design," Journal of Applied Statistics, Taylor & Francis Journals, vol. 41(9), pages 1903-1918, September.
    4. Wang, Jianjun & Ma, Yizhong & Ouyang, Linhan & Tu, Yiliu, 2016. "A new Bayesian approach to multi-response surface optimization integrating loss function with posterior probability," European Journal of Operational Research, Elsevier, vol. 249(1), pages 231-237.
    5. R Rajagopal & E del Castillo, 2007. "A Bayesian approach for multiple criteria decision making with applications in Design for Six Sigma," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 58(6), pages 779-790, June.

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