Research Commons
      • Browse 
        • Communities & Collections
        • Titles
        • Authors
        • By Issue Date
        • Subjects
        • Types
        • Series
      • Help 
        • About
        • Collection Policy
        • OA Mandate Guidelines
        • Guidelines FAQ
        • Contact Us
      • My Account 
        • Sign In
        • Register
      View Item 
      •   Research Commons
      • University of Waikato Theses
      • Higher Degree Theses
      • View Item
      •   Research Commons
      • University of Waikato Theses
      • Higher Degree Theses
      • View Item
      JavaScript is disabled for your browser. Some features of this site may not work without it.

      αₙ-Designs

      Ruggiero, Katya
      Thumbnail
      Files
      thesis.pdf
      6.552Mb
      Permanent link to Research Commons version
      https://hdl.handle.net/10289/14797
      Abstract
      This thesis defines a broad class of resolvable incomplete block designs for multifactor experiments, called αₙ-designs. A general methodology for their construction is described and is shown to be a natural extension of the method used by Patterson and Williams (1976) in their construction of α-designs. In fact, the class of α-designs are a special case of αₙ-designs with n = 1.

      The family of αₙ-designs was primarily developed for their use in factorial experiments. While they are particularly suitable for this purpose, for some combinations of design parameters they also provide more efficient designs than the best available α-designs.

      Algorithms for the generation of efficient designs require computationally expensive eigenvalue calculations. Therefore, considerable attention is devoted to the study of the structural properties of αₙ-designs and how these can be used to develop computationally fast algorithms. In this endeavour it is shown that the treatment concurrence and information matrices have an important property known as BⁿC-structure. This is used to derive a closed form mathematical expression for the average efficiency factor of any generalized interaction. It is further shown that this expression can be written recursively. These results, combined with the fact than an αₙ-design is completely specified by a small generating array, mean that computer search algorithms can be developed to quickly find highly efficient designs.

      A desirable feature in a factorial design is the property of orthogonal factorial structure. The family of αₙ-designs do not, in general, admit this property. However, another class of n-dimensional cyclic designs, known as n-cyclic designs, suitable for non-resolvable designs for factorial experiments are also considered in this thesis. They possess orthogonal factorial structure and include a sizeable subset of designs which are resolvable. These resolvable n-cyclic designs are shown to be αₙ-designs.

      The discovery and subsequent development of the family of αₙ-designs has stimulated a new set of interesting questions in relation to factorial experiments. These are discussed at the end of the thesis.
      Date
      2000
      Type
      Thesis
      Degree Name
      Doctor of Philosophy (PhD)
      Supervisors
      John, J.A.
      Publisher
      The University of Waikato
      Rights
      All items in Research Commons are provided for private study and research purposes and are protected by copyright with all rights reserved unless otherwise indicated.
      Collections
      • Higher Degree Theses [1714]
      Show full item record  

      Usage

      Downloads, last 12 months
      5,761
       
       

      Usage Statistics

      For this itemFor all of Research Commons

      The University of Waikato - Te Whare Wānanga o WaikatoFeedback and RequestsCopyright and Legal Statement