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Sequential third-order response surface designs

AUTHOR(S):

M. P. Iwundu and G. O. Agadaga

JOURNAL: Journal of Nigerian Statistical Association Vol.33, 2021
YEAR: 2021

ABSTRACT

The use of third-order response surface designs suggests experimental situations involving second-order lack-of-fits. New sequential third-order response surface designs are proposed for use in modeling third-order effects using very simple mathematical principles. The experimental runs admitted into the designs are hat matrix aided and the new designs show high design efficiencies. Grid formation is adopted as a principle of discretizing a continuous design space. For a cuboidal region in k dimensions, five grid levels are utilized and the associated 5^k grid points form the candidate set for consideration in design construction. The new sequential designs are augmentations of the standard central composite designs and are generated using block of points corresponding to some diagonal elements of the hat matrix. All designs studied in two and three variables have very good optimality properties


BIBLIOGRAPHY

Aanchal, N.A., Kanika, D.G. and Arun, G. (2016).Response Surface Methodology for Optimization of Microbial Cellulase Production, Romanian Biotechnological Letters. 21(5), 11832 – 11841.

Akhtar, M. and Prescott, P. (1986). Response Surface Designs Robust to Missing Observations, Communications in Statistics-Simulation and Computation, 15(2), 345 – 363.

Alaeddini, A., Murat, A., Yang, K. and Ankenmanc, B. (2013a). An Efficient Adaptive Sequential Methodology for Expensive Response Surface Optimization, Quality and Reliability Engineering International, 29 (6), 799–817. DOI: 10.1002/qre.1432.

Alaeddini, A., Yang, K., Murat, A. (2013b). ASRSM: A Sequential Experimental Design for Response Surface Optimization, Quality and Reliability Engineering International, 29(2), 241 – 258.


Arshad, H.M., Ahmad, T. and Akhtar, M. (2020). Some Sequential Third-Order Response Surface Designs, Communications in Statistics - Simulation and Computation, 49(7), 1872 – 1885.DOI: 10.1080/03610918.2018.1508700.

Arshad, H.M., Akhtar, M. and Gilmour, S.G. (2012). Augmented Box-Behnken Designs for Fitting Third-Order Response Surfaces, Communications in Statistics – Theory and Methods, 41(23), 4225 – 4239.

Bader, B., Yan, J. and Zhang, X. (2018).Automated Threshold Selection for Extreme Value Analysis via Ordered Goodness-of-Fit Tests with False Discovery Rate, The Annals of Applied Statistics, 12(1), 310–329.

Baker, F.D. and Bargmann, R.E. (1985).Orthogonal Central Composite Designs of the Third Order in the Evaluation of Sensitivity and Plant Growth Simulation Models, Journal of the American Statistical Association, 80(391), 574 – 579.

Balasubramanian, R.K. (2010). Heterogeneous Catalysis of Plant Derived Oils to Biodiesel, PhD Thesis Submitted to the Division of Environmental Science and Engineering, National University of Singapore. 

Bosque-Sendra, J.M., Pescarolo, S., Cuadros-Rodríguez, L., García-Campaña, A.M., Almansa-López, E.M. (2001). Optimizing Analytical Methods using Sequential Response Surface Methodology: Application to the Pararosaniline Determination of Formaldehyde, Fresenius Journal of Analytical Chemistry,369, 715 – 718. DOI: 10.1007/s002160100751.

Box, G.E.P.  and Wilson, K.B. (1951). On the Experimental Attainment of Optimum Conditions, Journal of the Royal Statistical Society, 13, 1–15.

Box, G.E.P. (1952). Multifactor Designs of First Order, Biometrika, 39, 49 – 57.

Box, G.E.P. (1954). The Exploration and Exploitation of Response Surfaces: Some General Considerations and Examples, Biometrics, 10(1),16-60. DOI: 10.2307/3001663.

Box, G.E.P. and Behnken, D.W. (1959). Simplex-Sum Designs a Class of Second Order Rotatable Designs Derivable from Those of First Order, Institute of Statistics Mimeograph Series No. 232.

Box, G.E.P. and Hunter, J.S. (1957). Multi-Factor Experimental Design for Exploring Response Surfaces, Annals of Mathematical Statistics, 28(1),195 – 241.

Castillo, F.A., Sweeney, J.D. and Zirk, W.E. (2004).Using Evolutionary Algorithms to Suggest Variable Transformations in Linear Model Lack-of-Fit Situations, In: Proceedings of the Congress on Evolutionary Computations, 556-560. https://ieeexplore.ieee.org/document/1330906.

Das, M.N. and Narasumham, V.L. (1962). Construction of Rotatable Designs Through Balanced Incomplete Block Designs, The Annals of Mathematical Statistics, 33, 1421 – 1439.

Derringer, G.C. (1969).Sequential Method for Estimating Response Surfaces, Industrial and Engineering Chemistry, 61(12), 6 – 13. 

Draper, N.R. (1960). Third Order Rotatable Designs in Three Dimensions, Annals of Mathematical Statistics, 31(4), 865 – 874. DOI:10.1214/aoms/1177705662. 

Gao, G.-M., Zou, H.-F., Liu, D.-R., Miao, L.-N., Gan, S.-C., An, B.-C., Xu, J.-J., Li, G.-H., and Shao, (2009). Synthesis of Ultrafine Silica Powders Based on Oil Shale Ash Fluidized Bed Drying of Wet-Gel Slurry, Fuel, 88(7), 1223- 1227.

Gardiner, D.A., Grandage, A.H.E. and Hader, R.J. (1959). Third Order Rotatable Designs for Exploring Response Surface, The Annals of Mathematical Statistics, 30, 1082 – 1096.




Ginsbourger, D. (2017). Sequential Design of Computer Experiments, Statistics Reference Online. DOI: 10.1002/ISBN.stat00999.pub9.

Hebble, T.I. and Mitchell, T.J. (1972).Repairing Response Surface Designs, Technometrics, 14(3), 767 – 779.

Hoaglin, D.C. and Welsch, R.E. (1978). The Hat Matrix in Regression and ANOVA, The American Statistician, 32(1), 17 – 22.

Huda, S. (1982). Some Third-Order Rotatable Designs in Three Dimensions, Annals of the Institute of Statistical Mathematics, 34, 365 – 371.

Iwundu, M.P. (2017). On the Compounds of Hat Matrix for Six-Factor Central Composite Design with Fractional Replicates of the Factorial Portion, American Journal of Computational and Applied Mathematics, 7(4), 95-114, DOI: 10.5923/j.ajcam.20170704.02.

Iwundu, M.P. (2018). Construction of Modified Central Composite Designs for Non-standard Models, International Journal of Statistics and Probability, 7(5), 95 – 119.DOI:10.5539/ijsp.v7n5p95.

Kahng, M.W. (2007). Leverages Measures in Nonlinear Regression, Journal of Korean Data and Information Science Society, 18(1), 229 – 235.

Khuri, A.I. (2017). A General Overview of Response Surface Methodology, Biomedical and Biostatistcs International Journal,5(3),87 – 93. DOI: 10.15406/bbij.2017.05.00133.

Koske, J.K., Kosgei, M.K. and Mutiso, J.M. (2011). A New Third Order Rotatable Design in Five Dimensions Through Balanced Incomplete Block Designs, Journal of Agriculture, Science and Technology, 13(1), 157 – 163.

Koukouvinos, C., Mylona, K., Simos, D.E. and Skountzou, A. (2009). An Algorithmic Construction of Four-Level Response Surface Designs, Communications in Statistics - Simulation and Computation, 38(10),2152 – 2160. DOI:10.1080/03610910903259634.

Lam, C.Q. (2008). Sequential Adaptive Designs in Computer Experiments for Response Surface Model Fit, A PhD Thesis submitted to the Ohio State University Columbus, OH, USA.

Landman, D., Simpson, J., Mariani, R., Ortiz, F. and Britcher, C. (2007).Hybrid Design for Aircraft Wind-Tunnel Testing Using Response Surface Methodologies, Journal of Aircraft, 44(4), 1214 – 1221.

Morshedi, A. and Akbarian, M. (2014). Application of Response Surface Methodology: Design of Experiments and Optimization: A Mini Review, Indian Journal of Fundamental and Applied Life Sciences, 4(S4), 2434 – 2439. 

Myers, R.H., Montgomery, D.C. and Anderson-Cook, C.M. (2009). Response Surface Methodology, Process and Product Optimization Using Designed Experiments,3rd Ed., Wiley, New York, NY.

Norulaini, N.A.N., Setiano, W.B., Zaidul, I.S.M., Nawi, A.H., Azizi, C.Y.M. and Omar, A.K.M. (2009). Effects of Supercritical Carbon Dioxide Extraction Parameters on Virgin Coconut Oils Yields and Medium-Chain Triglyceride Content, Food Chemistry, 116(1), 193 – 197. 

Oguaghamba, O.A. and Onyia, M.E. (2019). Modified and Generalized Full Cubic Polynomial Response Surface Methodology in Engineering Mixture Design, Nigerian Journal of Technology, 38(1), 52–59.

Peasura, P. (2015). Application of Response Surface Methodology for Modeling of Postweld Heat Treatment Process in a Pressure Vessel Steel ASTM A516 Grade 70,The Scientific World Journal, 2015, 1 – 8. DOI: http://dx.doi.org/10.1155/2015/318475.


Rotich, J.C., Kosgei, M.K. and Kerich, G.K. (2017). Optimal Third Order Rotatable Designs Constructed from Balanced Incomplete Block Design (BIBD), Current Journal of Applied Science and Technology, 22(3), 1 – 5.

SeshuBabu, P., DattatreyaRao, A.V., Anjaneyulu, G.V.S.R. and Srinivas, K. (2015). Cubic Response Surface Designs Using BIBD in Four Dimensions, Applied Mathematics and Sciences: An International Journal, 2(1), 17 – 21.

SeshuBabu, P., DattatreyaRao, A.V. and Srinivas, K. (2014). Construction of Third Order Slope Rotatable Designs Using BIBD, International Review of Applied Engineering Research. 4(1), 89 – 96.

Srisuradetchai, P. (2015). Robust Response Surface Designs Against Missing Observations, PhD Thesis, Montana State University Bozeman.

Yang, Y. (2008).Multiple Criteria Third-Order Response Surface Design and Comparison, M.Sc. Dissertation Submitted to FAMU-FSU College of Engineering, Florida State University.




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