Finding Robust Response Surface Designs With Blocking Using a Model-Weighted A-Optimality Criterion

Article Sidebar

PDF
DOI: https://doi.org/10.28924/2291-8639-22-2024-150
Published: Sep 2, 2024
Cite as:
Peang-or Yeesa, Sudarat Nidsunkid, Finding Robust Response Surface Designs With Blocking Using a Model-Weighted A-Optimality Criterion, Int. J. Anal. Appl., 22 (2024), 150.

Main Article Content

Peang-or Yeesa, Sudarat Nidsunkid

Abstract

This paper proposes a new approach to finding robust response surface designs that can accommodate potential model misspecifications. To achieve this, experimental designs that are robust across all potential models were considered prior to data collection. Blocking effects were combined into all possible models, and the set of all reduced models was obtained using the weak heredity principle. The objective of this study was to propose the use of the geometric mean of A-optimalities as a new weighted A-optimality criterion for finding robust response surface designs. Both a genetic algorithm (GA) and an exchange algorithm (EA) were employed to optimize the weighted A-optimality criterion and compared with the widely used central composite design. The weighted A-optimal designs generated by GA and EA in this study had higher Aw and A-efficiencies than CCD, and the Aw-optimal designs generated by the GA were as or more efficient than the EA.

Article Details

References

  1. A.C. Atkinson, A.N. Donev, R.D. Tobias, Optimum Experimental Designs, with SAS, Oxford University Press, Oxford, 2007. https://doi.org/10.1093/oso/9780199296590.001.0001.
  2. J.J. Borkowski, E.S. Valeroso, Comparison of Design Optimality Criteria of Reduced Models for Response Surface Designs in the Hypercube, Technometrics. 43 (2001), 468–477. https://doi.org/10.1198/00401700152672564.
  3. J.J. Borkowski, P. Turke, B. Chomtee, Using Weak and Strong Heredity to Generate Weighted Design Optimality Criteria for Response Surface Designs, J. Stat. Theory Appl. 10 (2011), 468–477.
  4. G.E.P. Box, J.S. Hunter, W.G. Hunter, Statistics for Experimenters: Design, Innovation, and Discovery, 2nd ed, Wiley-Interscience, Hoboken, 2005.
  5. A. Chairojwattana, S. Chaimongkol, J.J. Borkowski, Using Genetic Algorithms to Generate Dw and Gw-Optimal Response Surface Designs in the Hypercube, Thailand Statistician. 15 (2017), 157–166.
  6. H. Chipman, Bayesian Variable Selection With Related Predictors, Canad. J. Stat. 24 (1996), 17–36. https://doi.org/10.2307/3315687.
  7. R.D. Cook, C.J. Nachtrheim, A Comparison of Algorithms for Constructing Exact D-Optimal Designs, Technometrics 22 (1980), 315–324. https://doi.org/10.1080/00401706.1980.10486162.
  8. V.V. Fedorov, Theory of Optimal Experiments, Academic Press, New York, 1972.
  9. J.H. Holland, Adaptation in Natural and Artificial System: An Introductory Analysis With Applications to Biology Control, and Artificial Intelligence, University of Michigan Press, Oxford, 1975.
  10. W. Limmun, J.J. Borkowski, B. Chomtee, Weighted A-Optimality Criterion for Generating Robust Mixture Designs, Comp. Ind. Eng. 125 (2018), 348–356. https://doi.org/10.1016/j.cie.2018.09.002.
  11. W. Limmun, B. Chomtee, J.J. Borkowski, The Construction of a Model-Robust IV-Optimal Mixture Designs Using a Genetic Algorithm, Math. Comp. Appl. 23 (2018), 25. https://doi.org/10.3390/mca23020025.
  12. W. Limmun, B. Chomtee, J.J. Borkowski, Using Geometric Mean to Compute Robust Mixture Designs, Qual. Reliab. Eng. 37 (2021), 3441–3464. https://doi.org/10.1002/qre.2927.
  13. S. Mahachaichanakul, P. Srisuradetchai, Applying the Median and Genetic Algorithm to Construct D- and GOptimal Robust Designs Against Missing Data, Appl. Sci. Eng. Progress. 12 (2019), 3–13. https://doi.org/10.14416/j.ijast.2018.10.002.
  14. R.K. Meyer, C.J. Nachtsheim, The Coordinate-Exchange Algorithm for Constructing Exact Optimal Experimental Designs, Technometrics 37 (1995), 60–69. https://doi.org/10.1080/00401706.1995.10485889.
  15. T.J. Mitchell, An Algorithm for the Construction of "D-Optimal" Experimental Designs, Technometrics 16 (1974), 203–210. https://doi.org/10.2307/1267940.
  16. T.J. Mitchell, Computer Construction of "D-Optimal" First-Order Designs, Technometrics 16 (1974), 211–220. https://doi.org/10.2307/1267941.
  17. D.C. Montgomery, Design and Analysis of Experiments, John Wiley & Sons, Hoboken, 2013.
  18. R.H. Myers, D.C. Montgomery, C.M. Anderson-Cook, Response Surface Methodology: Process and Product Optimization Using Designed Experiments, John Wiley & Sons, Hoboken, 2016.
  19. A.F. Shahraki, R. Noorossana, A Combined Algorithm for Solving Reliability-Based Robust Design Optimization Problems, J. Math. Comp. Sci. 7 (2013), 54–62.
  20. H.P. Wynn, Results in the Theory and Construction of D-Optimum Experimental Designs, J. R. Stat. Soc. Ser. B: Stat. Methodol. 34 (1972), 133–147. https://doi.org/10.1111/j.2517-6161.1972.tb00896.x.
  21. P. Yeesa, P. Srisuradetchai, J.J. Borkowski, Model-Robust G-Optimal Designs in the Presence of Block Effects, Appl. Sci. Eng. Progress. 12 (2019), 198–208.
  22. P. Yeesa, P. Srisuradetchai, J.J. Borkowski, A Weighted D-Optimality Criterion for Constructing Model-Robust Designs in the Presence of Block Effects, Songklanakarin J. Sci. Technol. 42 (2020), 1259–1273.