Design Model

The way that the factors relate to each other to produce the measured response is postulated by the Design Model. The model presumes that the factors and their interactions have independent additive effects (Usually referred to as linear in the coefficients). The terms may reveal a functional relationship among the response and the factors, if one exists.

The model has a general validity in that many phenomena may be approximated by a general linear polynomial. The general polynomial model is truncated for use in regression analysis. Most DOE software allows the use of linear and quadratic terms for main factors, for two-factor interaction terms and for three-factor interaction terms. The remaining terms in the general polynomial are all combined into the truncation error term. Both transforms on the response or on the factors may be used to reduce nonlinear terms to linear terms of a transformed parameter.

When a nonlinear response to the factors is expected, at least three levels of each factor are required. It is usually true that Central Composite or Box-Behnken designs are more efficient than factorial designs. Some nonlinear responses are better fitted by transforming either the factors or the response(s) or by combining two or more responses.

Experimental Response = Fitted Model Response + Error

The fitted DOE model is shown below, where the model is restricted to no more than 3-factor interactions (triquadratic) and the nonlinear terms are restricted to quadratic power (p <= 2, q <= 2, r <= 2). The simplest model has only the mean and linear terms, with no provision for estimating the error.