Fractional Polynomial Response Surfaces

Abstract

Polynomial response surface models have been used successfully in many experiments to improve understanding of and to optimise processes. However, sometimes the inflexibility of shapes of surfaces provided by polynomials hinders interpretation. A generalised family of models, fractional polynomials, have recently been used successfully for modelling observational data. It will be shown how these can be useful in response surface experimentation. One disadvantage of fractional polynomials is that the standard response surface designs are not well suited to fitting them. A procedure for producing optimal Bayesian designs for fitting these models will be described. It uses a computer algebra package to obtain the general form of the optimality criterion, sampling from the prior distributions of parameters to approximate the criterion and an exchange algorithm to find optimal designs.