Design Criterion for Estimating Mean and Variance Functions

In an industrial process, the proper objective is to find the optimal operating conditions with minimum process variability around the target. Vining and Myers(1990) suggest to use the separate model for the mean response and the process varian linear predictor ${\tau}_i={\log}\;{\sigma}^2_i$ is unknown and should be estimated. Noting that the variance of $\hat{{\tau}_i}$ is heterogeneous, another appropriate D-optimality criterion $D_3$ based on the method of generalized least squares is proposed in this paper.