The Choice of the Parameter Values in a Multivariate Model of a Second Order Surface with Heteroschedastic Error

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 2nd order model, with a heteroschedastic error. The procedure consists of two steps. In the first step an experimental design (we consider a three level full factorial design, for simplicity) is performed in the feasible space X of the control factors to estimate the parameters characterizing the response surface of the mean. Then a second experimental design is performed on a target set A, subset of X satisfying the condition on the average of Y(x). This second step determines the choice of x using a classification criterion based on the ordering of the sample mean squared errors. In both steps the model parameters are estimated by an iterative method.