The choice of the parameter values in a multivariate model of a second order surface with heteroscedastic error

Abstract

The paper describes an experimental procedure to choose the values for a multivariate vector x under these conditions: average of Y (x) equal to a target value and least variance of Y (x), linked to x by a second order model with a heteroscedastic error. The procedure consists of two steps. In the first step an experimental design is performed in the feasible space Χ of the control factors to estimate, by an iterative method, the parameters characterizing the response surface of the mean. Then a second experimental design is performed on a set A, subset of Χ satisfying a condition on the average of Y (x). This second step determines the choice of x by using a classification criterion based on the ordering of the sample mean squared errors. The research belongs to the theory of optimal design of experiments [2], that is employed in the Taguchi Methods, used in off-line control [6]. © Springer-Verlag Berlin Heidelberg 2011.