The methods of optimum experimental design are applied to models in which the variance, as well as the mean, is a parametric function of explanatory variables. Extensions to standard optimality theory lead to designs when the parameters of both the mean and the variance functions, or the parameters of only one function, are of interest. The theory also applies whether the mean and variance are functions of the same variables or of different variables, although the mathematical foundations differ. The example studied is a second-order two-factor response surface for the mean with a parametric nonlinear variance function. The theory is used both for constructing designs and for checking optimality. A major potential for application is to experimental design in off-line quality control.
Bibliographical noteFunding Information:
* R. D. Cook is Professor, Department of Applied Statistics, University of Minnesota, St. Paul 55108. A. C. Atkinson is Professor, Department of Statistics, London School of Economics and Political Science, London WCZA 2AE, U.K. This work was supported in part by grants from the National Science Foundation awarded to R. D. Cook. It was started when A. C. Atkinson was a visiting Professor at the Department of Applied Statistics, University of Minnesota. Professor Atkinson is grateful to the Staff Research Fund of the London School of Economics for support toward the completion of this research. The authors thank the referees for their help on an earlier version of this article.
Copyright 2015 Elsevier B.V., All rights reserved.
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