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Activity Number: 329
Type: Invited
Date/Time: Tuesday, August 6, 2013 : 10:30 AM to 12:20 PM
Sponsor: Section on Physical and Engineering Sciences
Abstract - #306954
Title: Optimal Split-Plot Designs for Fixed-Effect and Variance-Component Estimation
Author(s): Peter Goos*+ and Kalliopi Mylona and Bradley A. Jones
Companies: University of Antwerp and University of Southampton and JMP Division of SAS Institute Inc.
Keywords: Bayesian optimal design ; restricted maximum likelihood estimation ; variance component estimation ; composite criterion ; Gaussian quadrature
Abstract:

Many industrial experiments involve restrictions on the randomization. The most commonly used experimental designs in those cases are blocked designs and split-plot designs, where the experimental runs are performed in groups. In general, modeling data from blocked and split-plot response surface experiments requires the use of generalized least squares and the estimation of two variance components. The literature on the optimal design of blocked and split-plot response surface experiments, however, focuses entirely on the precise estimation of the fixed factor effects and completely ignores the necessity to estimate the variance components as well. To overcome this problem, we propose a new Bayesian optimal design criterion which focuses on both the variance components and the fixed effects. A novel feature of the criterion is that it incorporates prior information about the variance components through log-normal or beta prior distributions. In our algorithm for generating optimal blocked and split-plot designs, we implement efficient quadrature approaches for the numerical approximation of the new optimal design criterion.


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