A Mixed Integer Linear Programming Model for Finding Optimum Operating Conditions of Experimental Design Variables Using Computer-Aided Optimal Experimental Designs
Abstract
Computer-aided
optimal experimental designs are an effective quality improvement tool that
provides insights of information under various quality engineering problems. In
the literature, considerable attention has been focused on maximizing the
determinant of the information matrix in order to generate optimal design
points. However, minimizing the average prediction based on the I-optimality criterion is more useful
than commonly used D-optimality
criterion for a number of situations. In this paper, special experimental
design situations are explored where both qualitative and quantitative input
variables are considered for an irregular design space with the pre-specified
number of design points and the first-order polynomial model. In addition, this
paper lays out the algorithmic foundations for the proposed D- and I-optimality criteria embedded mixed integer linear programming
models in order to obtain optimal operating conditions using the first-order
response functions. Comparative studies are also conducted. Finally, the
proposed models are superior to the traditional counterparts.
Keywords
References
- Allen, T. T., & Tseng, S. H. (2011). Variance plus bias optimal response surface designs with qualitative factors applied to stem choice modeling. Quality and Reliability Engineering International, 27(8), 1199-1210.
- Arvidsson, M., & Gremyr, I. (2008). Principles of robust design methodology. Quality and Reliability Engineering International, 24(1), 23-35.
- Borkowski, J. J. (2003). A comparison of prediction variance criteria for response surface designs. Journal of Quality Technology, 35(1), 70-77.
- Box, G. E., & Draper, N. R. (1959). A basis for the selection of a response surface design. Journal of the American Statistical Association, 54(287), 622-654.
- Chatterjee, K., Drosou, K., Georgiou, S. D., & Koukouvinos, C. (2018). Response modelling approach to robust parameter design methodology using supersaturated designs. Journal of Quality Technology, 50(1), 66-75.
- Cook, R. D., & Nachtrheim, C. J. (1980). A comparison of algorithms for constructing exact D-optimal designs. Technometrics, 22(3), 315-324.
- Copeland, K. A., & Nelson, P. R. (1996). Dual response optimization via direct function minimization. Journal of Quality Technology, 28(3), 331-336.
- Del Castillo, E., & Montgomery, D. C. (1993). A nonlinear programming solution to the dual response problem. Journal of Quality Technology, 25(3), 199-204.
- Draper, N. R. (1982). Center points in second—order response surface designs. Technometrics, 24(2), 127-133.
- John, R. S., & Draper, N. R. (1975). D-optimality for regression designs: a review. Technometrics, 17(1), 15-23.