Some Small Response Surface Designs for Three-Factor Experiments
Virgilio D. Espina1, Rosadelima V. Lopez2, Daisy Lou L. Polestico3
1Department of Mathematics, University of San Carlos, Cebu, Central Visayas, Philippines; 2Department of Mathematics, MSU - Iligan Institute of Technology, Iligan, Lanao del Norte, Philippines; 3Department of Mathematics, MSU - Iligan Institute of Technology, Iligan, Lanao del Norte, Philippines

Four readily available second-order small response surface designs for three-factor experiments are examined and compared in order to find an alternative design for experiments with limited resources. In this paper, the prediction variances of Roquermore's three-factor hybrid designs and Draper-Lin's small composite design are investigated over the experimental region using box plot and fraction design space (FDS) plot. For each spherical region, the replication of center and axial points are compared. The Box plot and Fraction Design Space plot shows that increasing the number of center and axial points will result in a decrease of standard error of D311B; will also result in a more stable prediction variance and will also decrease the spread of dispersion of the prediction variance. These results suggest that D311B is more efficient and is preferable for three-factor experiments with inadequate resources.

Bibliography:

Anderson-Cook, C.M., Borror C.M., Montgomery, D.C. Response Surface Design Evaluation and Comparison.Journal of Statistical Planning and Inference.vol. 139.pp. 629 - 641.2009.

Borkowski, J.J. A comparison of prediction variance criteria for response surface designs. Journal of Quality Technology.vol 35 no. 1. 2003.

Box G.E.P., Draper N.R. A Basis for the Selection of a Response Surface Design.Journal of the American Statistical Association. vol. 54 No. 287, pp. 622-654. 1959.

Draper N.R., Lin D.K.J. Small Response-Surface Designs. Technometrics.vol 32 no 2, pp187-194.1990.

Giovannitti-Jensen A., Raymond M.H. Graphical Assessment of the Prediction Capability of Response Surface Designs. Technometrics.vol 31 no 2, pp. 159-171.1989.

Hartley, H.O. Smallest Composite Designs for Quadratic Response Surfaces. Biometrics.vol 15 no 4, pp. 611 - 624. 1959.

Roquemore, K.G. Hybrid Designs for Quadratic Response Surfaces.Technometrics.vol 18 no 4, pp. 419 – 423. 1976.

Zahran A., Anderson-Cook C.M., Myers R.H. Fraction of Design Space to Assess Prediction Capability of Response Surface Designs. American Society for Quality.vol 35 no. 4. 2003.

Keywords: Axial and center points; Draper-Lin small composite design; Fraction design space plot; Roquermore hybrid designs

Biography: Virjil, a practicing statistician, has been collaborating scientific researches for almost a decade. Most of his collaborations were in the field of renewable energy, materials science and biotechnology. His interest is response surface methodology and is currently one of the research collaborators of the Commission on Higher Education - Zonal Research Center Grant in Aid project. He is currently teaching mathematics and statistics at the University of San Carlos, Cebu City, Philippines.