OPTIMAL RESPONSE SURFACE DESIGNS IN THE PRESENCE OF DISPERSION EFFECTS 6 the D-optimal designs use the three factorial loca- ance ratios increase.although at a slow rate.and the standard design is remarkably efficient (in term suse the tim The interaction model requires at least four dis signs for the m ocation D-and ficiencies of the standard design decrease as the vari- cations. of larges mallest variance.Hence the f-efficiency of the stan the f-optimal designs First-Order Model so again the I-optimal designs are nearly invariant to the magnitude of the dispersion effects. For the second-order model both the D.and I optimal designs require runs at the factorial loca Efficiency100.0097.3291.2085.1082.4379.41 sandaditionmlkathee ocations with the quire runs in the design center.The D-optimal de signs for the mag designs Efficieney 100.0097.8591.9384.81772568.62 I-optimal designs are more invariant to the magni- tude of the dispersion effects,and the InteractionModel fectThe D-ecnc mplving that Do the standard design can be improved upon,particu- larly for severe dispersion effects Efficiency 100.00100.00100.00100.00100.00100.00 Linear-Quadratic t variance located in the design center.Facto E伍ciency c(1)and (1 the 100.0094.8187.50773169.8459.17 the Second-Order Model first-order model,the optimal designs now require uns at all four fact l de timal designs with more runs at the locations of large variance.The Efficiency 85.0682.5379.0874.5871.6067.61 ign is highly efficient 18 For the interactio model.the standard desig Efficiency100.0098.2197.0294.6691.7486.52 optimal designs place runs at all four factorial loca tions.again favoring the locations of large variance. Vol.29.No.1.January 199 Reproduced with permission of the copyright owner.Further reproduction prohibited without permission.Reproduced with permission of the copyright owner. Further reproduction prohibited without permission