Response Surface Designs for Factors at Two and Three Levels and at Two and Four Levels

The choice of an experimental design suitable for fitting a graduating polynomial can be made according to a number of criteria, depending on the problem involved. Difficulties arise when, although the factors are continuous in nature, the number of levels is specified by some external considerations. For example, if some factors can be examined at only two levels, the graduating function cannot include quadratic terms in those variables, but all second order terms for variables to be examined at three or more levels can be permitted. For such cases, a restricted model and special experimental designs are needed. This paper considers the problem when there are some factors at two levels and some factors at three levels, and when there are some factors at two levels and some factors at four levels.