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Some Notes on Types of Symmetry for Crossover Designs

In: Mindful Topics on Risk Analysis and Design of Experiments

Author

Listed:
  • A. S. Hedayat

    (University of Illinois)

  • Wei Zheng

    (University of Tennessee)

Abstract

Crossover designs are used to assign multiple treatments to the same unit over a period of time. In the search of optimal crossover designs, approximate design theory emerged to be a powerful tool over the last two decades. In its development, the idea of symmetrization plays a crucial role (Kushner 1997). While the construction of exact symmetric designs from the approximate design theory is relatively straightforward; however, to achieve the symmetry, a large number of units is typically required. There exist evidence that concept of symmetry could be generalized. This paper extracts and organizes some key ideas scattered in the literature and formulates them into a systematic way of constructing an important type of symmetric designs. We also give a survey of recent advances on crossover designs and related studies, where new designs could be derived by the methods laid out in this paper.

Suggested Citation

  • A. S. Hedayat & Wei Zheng, 2022. "Some Notes on Types of Symmetry for Crossover Designs," Springer Books, in: Jürgen Pilz & Teresa A. Oliveira & Karl Moder & Christos P. Kitsos (ed.), Mindful Topics on Risk Analysis and Design of Experiments, pages 95-112, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-06685-6_8
    DOI: 10.1007/978-3-031-06685-6_8
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