Title page for etd-0710103-174745


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URN etd-0710103-174745
Author Hsiang-Ling Hsu
Author's Email Address hsuhl@math.nsysu.edu.tw
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Department Applied Mathematics
Year 2002
Semester 2
Degree Master
Type of Document
Language English
Title Robust D-optimal designs for mixture experiments in Scheffe models
Date of Defense 2003-06-06
Page Count 54
Keyword
  • invariant symmetric block matrices
  • Complete class
  • Dr-efficiency
  • equivalence theorem
  • convex combination
  • Abstract A mixture experiment is an experiment in which the
    q-ingredients {xi,i=1,...,q} are nonnegative and subject to the simplex restriction sum_{i=1}^q x_i=1 on the (q-1)-dimensional probability simplex S^{q-1}. In this work, we investigate the robust D-optimal designs for mixture experiments with consideration on uncertainties in the Scheffe's linear, quadratic and cubic model without 3-way effects. The D-optimal designs for each of the Scheffe's models are used to find the robust D-optimal designs. With uncertianties on the Scheffe's linear and quadratic models, the optimal convex combination of the two model's D-optimal designs can be proved to be a robust D-optimal design. For the case of the Scheffe's linear and cubic model without 3-way effects, we have some numerical results about the robust D-optimal designs, as well as that for Scheffe's linear, quadratic and cubic model without 3-way effects. Ultimately, we discuss the efficiency of a maxmin type criterion D_r under given the robust D-optimal designs for the Scheffe's linear and quadratic models.
    Advisory Committee
  • Fu-Chuen Chang - chair
  • Chwen-Ming Chang - co-chair
  • Grace Shwu-Rong Shieh - co-chair
  • Mong-Na Lo Huang - advisor
  • Files
  • etd-0710103-174745.pdf
  • indicate access worldwide
    Date of Submission 2003-07-10

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