Comparison of designs in presence of a possible correlation in observations

We often assume the standard linear model with uncorrelated observations for comparison of designs without realizing a possible presence of correlation in observations. In this paper we present several change of variance functions including the one given in Zhou (2001) for comparing designs in presence of possible correlation in observations. We find a design by minimizing one of our proposed change of variance functions in a simple response surface setup. We then compare its performance with all variance design, all bias design, and the design making the average variance equal to the average squared bias. We also compare a second order rotatable design with a non-rotatable design. The rotatable design is better than the non-rotatable design with respect to A-, D-, and E- optimality criterion functions under the standard linear model with uncorrelated observations. We observe that the rotatable design may not perform better than the non-rotatable design with respect to the change of variance functions. We present some important properties of the change of variance functions. We find that the A-optimum designs may perform poorly with respect to a change of variance function.