ABSTRACT
In Chapter 1 it was noted that in a response surface investigation, one of the objectives is the empirical determination of the functional relationship between the true mean response and a set of input variables. This relationship is represented by an unknown response function, which is assumed to be continuous in the input variables within some specified region of interest. Polynomial models are employed as approximating functions. In practice, low-degree polynomials are favored over high-degree polynomials because of their simpler form (fewer number of terms), particularly when one is studying the response over a small subregion, R, of the factor space. Over a larger region, for example, the operability region O or possibly the entire factor space, such low-degree polynomial representations may be inadequate and unrealistic due to the presence of lack of fit caused by higher-order terms in the true mean response model. In this case, a higher-degree polynomial is needed.
