Fractional factorial designs are a popular choice in designing experiments for
studying the effects of multiple factors simultaneously. The first step in planning an
experiment is the selection of an appropriate fractional factorial design. An appro-
priate design is one that has the statistical properties of interest of the experimenter
and has a small number of runs. This requires that a catalog of candidate designs
be available (or be possible to generate) for searching for the "good" design. In the
attempt to generate the catalog of candidate designs, the problem of design isomor-
phism must be addressed. Two designs are isomorphic to each other if one can be
obtained from the other by some relabeling of factor labels, level labels of each factor
and reordering of runs. Clearly, two isomorphic designs are statistically equivalent.
Design catalogs should therefore contain only designs unique up to isomorphism.
There are two computational challenges in generating such catalogs. Firstly,
testing two designs for isomorphism is computationally hard due to the large number
of possible relabelings, and, secondly, the number of designs increases very rapidly
with the number of factors and run-size, making it impractical to compare all designs
for isomorphism. In this dissertation we present a new approach for tackling both
these challenging problems. We propose graph models for representing designs and
use this relationship to develop efficient algorithms. We provide a new efficient iso-
morphism check by modeling the fractional factorial design isomorphism problem as
graph isomorphism problem. For generating the design catalogs efficiently we extend a result in graph isomorphism literature to improve the existing sequential design
catalog generation algorithm.
The potential of the proposed methods is reflected in the results. For 2-level
regular fractional factorial designs, we could generate complete design catalogs of run
sizes up to 4096 runs, while the largest designs generated in literature are 512 run
designs. Moreover, compared to the next best algorithms, the computation times
for our algorithm are 98% lesser in most cases. Further, the generic nature of the
algorithms makes them widely applicable to a large class of designs. We give details of
graph models and prove the results for two classes of designs, namely, 2-level regular
fractional factorial designs and 2-level regular fractional factorial split-plot designs,
and provide discussions for extensions, with graph models, for more general classes
of designs.
| Identifer | oai:union.ndltd.org:tamu.edu/oai:repository.tamu.edu:1969.1/ETD-TAMU-2009-12-7345 |
| Date | 2009 December 1900 |
| Creators | Shrivastava, Abhishek Kumar |
| Contributors | Ding, Yu |
| Source Sets | Texas A and M University |
| Language | en_US |
| Detected Language | English |
| Type | Book, Thesis, Electronic Dissertation, text |
| Format | application/pdf |
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