Experimental Designs for Estimating Both Mean and Variance Functions

Abstract

Statisticians are increasingly finding applications which require separate linear models for a response of interest and this response's variance. A crucial question then becomes what are reasonable experimental strategies which will allow the estimation of both of these functions. This paper pursues two distinct approaches: a one-step approach which, in the absence of any information about the process variance, initially assumes that the process variance is constant over the region of interest; and a one-step, semi-Bayesian approach which attempts to develop an appropriate experimental plan in light of prior information about the nature of the variance function. These two approaches are compared in a simulation study to illuminate their relative advantages and disadvantages. An example illustrates the proposed methodology.

• D-Optimality
• Multiple Responses
• Response Surface Methodology
• Simultaneous Optimization
• Taguchi Methods

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Notes on contributors

G. Geoffrey Vining

Dr. Vining is an Associate Professor in the Department of Statistics. He is a Senior Member of ASQC.

Diane Schaub

Dr. Schaub is an Assistant Professor in the Department of Industrial and Systems Engineering. She is a Senior Member of ASQC.