<P> Spherical designs are discussed by Kiefer and by Hardin and Sloane . </P> <P> Mixture experiments are discussed in many books on the design of experiments, and in the response - surface methodology textbooks of Box and Draper and of Atkinson, Donev and Tobias . An extensive discussion and survey appears in the advanced textbook by John Cornell . </P> <P> Some extensions of response surface methodology deal with the multiple response problem . Multiple response variables create difficulty because what is optimal for one response may not be optimal for other responses . Other extensions are used to reduce variability in a single response while targeting a specific value, or attaining a near maximum or minimum while preventing variability in that response from getting too large . </P> <P> Response surface methodology uses statistical models, and therefore practitioners need to be aware that even the best statistical model is an approximation to reality . In practice, both the models and the parameter values are unknown, and subject to uncertainty on top of ignorance . Of course, an estimated optimum point need not be optimum in reality, because of the errors of the estimates and of the inadequacies of the model . </P>

Difference between factorial design and response surface methodology