Taguchi parameter design by second-order response surfaces

The application of response surface methods for the design and analysis of Taguchi parameter design experiments is extensively discussed in a paper by Myers, Khuri and Vining (The American Statistician, 46, 131-139 (1992)). To illustrate the use of response surface analysis, much attention is given in that paper to a response model that is linear in the noise factors. In practice, such a model is often of limited use, since quadratic effects of, or interactions among, noise factors cannot be modelled. In this paper, second-order response surfaces in the noise factors are considered, so that these limitations are eliminated. Furthermore, the idea of design factors with noise is explained and it is shown that these can also be included in the model for the process variance. An example of a Box-Behnken experiment with noise factors is presented to show the usefulness of these extensions in practice.