Title page for ETD etd-03302005-194026


Type of Document Dissertation
Author Parker, Peter A.
URN etd-03302005-194026
Title Response Surface Design and Analysis in the Presence of Restricted Randomization
Degree PhD
Department Statistics
Advisory Committee
Advisor Name Title
Kowalski, Scott M. Committee Co-Chair
Vining, G. Geoffrey Committee Co-Chair
Anderson-Cook, Christine M. Committee Member
Reynolds, Marion R. Jr. Committee Member
Woodall, William H. Committee Member
Keywords
  • Response Surface Methodology
  • Restricted Randomization
  • Split-Plot Design
  • Equivalent Estimation
  • Box-Behnken
  • Central Composite
Date of Defense 2005-03-29
Availability unrestricted
Abstract
Practical restrictions on randomization are commonplace in industrial experiments due to the presence of hard-to-change or costly-to-change factors. Employing a split-plot design structure minimizes the number of required experimental settings for the hard-to-change factors. In this research, we propose classes of equivalent estimation second-order response surface split-plot designs for which the ordinary least squares estimates of the model are equivalent to the generalized least squares estimates. Designs that possess the equivalence property enjoy the advantages of best linear unbiased estimates and design selection that is robust to model misspecification and independent of the variance components. We present a generalized proof of the equivalence conditions that enables the development of several systematic design construction strategies and provides the ability to verify numerically that a design provides equivalent estimates, resulting in a broad catalog of designs. We explore the construction of balanced and unbalanced split-plot versions of the central composite and Box-Behnken designs. In addition, we illustrate the utility of numerical verification in generating D-optimal and minimal point designs, including split-plot versions of the Notz, Hoke, Box and Draper, and hybrid designs. Finally, we consider the practical implications of analyzing a near-equivalent design when a suitable equivalent design is not available. By simulation, we compare methods of estimation to provide a practitioner with guidance on analysis alternatives when a best linear unbiased estimator is not available. Our goal throughout this research is to develop practical experimentation strategies for restricted randomization that are consistent with the philosophy of traditional response surface methodology.
Files
  Filename       Size       Approximate Download Time (Hours:Minutes:Seconds) 
 
 28.8 Modem   56K Modem   ISDN (64 Kb)   ISDN (128 Kb)   Higher-speed Access 
  Balanced_BBDs.xls 116.22 Kb 00:00:32 00:00:16 00:00:14 00:00:07 < 00:00:01
  Balanced_CCDs.xls 169.47 Kb 00:00:47 00:00:24 00:00:21 00:00:10 < 00:00:01
  Balanced_Dopt_SCD_Equiradial.xls 76.80 Kb 00:00:21 00:00:10 00:00:09 00:00:04 < 00:00:01
  Catalog_Description.pdf 22.61 Kb 00:00:06 00:00:03 00:00:02 00:00:01 < 00:00:01
  Dissertation_PAP.pdf 461.93 Kb 00:02:08 00:01:05 00:00:57 00:00:28 00:00:02
  Equivalent_SplitPlot_Designs.pdf 213.89 Kb 00:00:59 00:00:30 00:00:26 00:00:13 00:00:01
  Minimal_Point_Designs.xls 251.90 Kb 00:01:09 00:00:35 00:00:31 00:00:15 00:00:01
  Unbalanced_BBDs.xls 81.41 Kb 00:00:22 00:00:11 00:00:10 00:00:05 < 00:00:01
  Unbalanced_CCDs.xls 51.71 Kb 00:00:14 00:00:07 00:00:06 00:00:03 < 00:00:01
  Unbalanced_SCDs.xls 20.99 Kb 00:00:05 00:00:02 00:00:02 00:00:01 < 00:00:01

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