LE3 .A278 2013

2013

Ranjan, Pritam
Mendivil, Franklin

Acadia University

Bachelor of Science

Honours

Mathematics and Statistics

Mathematics & Statistics

Full factorial and fractional factorial designs with randomization restrictions are often used for designing industrial experiments when complete randomization of the trials is impractical. Ranjan, Bingham and Dean (2009) and Ranjan, Bingham and Muk- erjee (2010) developed a uni ed theory for the construction of these designs using a projective geometric formulation. They established that the existence of 2p factorial designs with randomization restrictions correspond to the existence of partial spreads and stars of the projective space PG(p 􀀀 1; 2). The designs obtained can be ranked using criteria like maximum resolution, minimum aberration, number of clear e ects, and so on. In order to nd the best design under a speci ed ranking criterion, it is critical to rst check if two designs are isomorphic (i.e., essentially the same) or not. In this thesis, we rst propose a de nition of the isomorphism of two spreads, and then we develop several algorithms for checking isomorphism of spread and star based designs. These algorithms are e cient because they employ fast techniques for checking equivalence of spreads and reducing the search space of possible relabellings.

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https://scholar.acadiau.ca/islandora/object/theses:1039