Response-Surface Designs for Quantitative and Qualitative Variables

Abstract

When some variables are quantitative and some qualitative in a response-surface context, standard designs may not be suitable. The reasons for this are illuminated. Some alternative designs are discussed. Every n-point design provides n linearly independent estimation contrasts. Some of these, p say, are needed to estimate the p parameters of the postulated model. The remaining n — p linearly independent estimation contrasts are available to estimate pure error (if used) and to test for lack of fit, either overall or in particular ways. The key to choosing a good design is to use the available degrees of freedom well, given certain assumptions about the model to be fitted. When there is also uncertainty about the model assumptions, dogmatic design advice is not possible. Sound guidelines are available, however, and these are presented and illustrated.

KEY WORDS:

• Classification variable
• Composite design
• Dummy variable
• Experimental design
• Factorial design