ALGEBRAIC METHODS FOR CONSTRUCTION OF MIXED ORTHOGONAL ARRAYS

Nguyen Van Minh Man, Scott H. Murray

Abstract


Orthogonal arrays (OAs) of strength t (also called t-balanced fractional
designs) are difficult to construct, but they have useful properties
that can be employed in the theory of experimental design and in practical
applications to statistical quality management.
Specifically, strength 3 OAs permit estimation of all the main effects of
the experimental factors, without confounding them with the two-factor
interactions. Strength 4 OAs allow us to also separately estimate all twofactor
interactions. These arrays are in great demand not only in wellknown
areas like statistical quality control of industries and services [12],
software engineering [13], but also in emerging and fast-developed areas
such as computational biology, drug designs and/or medical sciences, in
particular DNA micro-array experiments [6, 21].
In this paper, we introduce some new methods for constructing mixed
orthogonal arrays of strength t, with a given parameter set of run-size
and factor levels. A few new arrays with run size up to 100 have been
found with the proposed methods.

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