TITLE:
Enumeration of Strength Three Orthogonal Arrays and Their Implementation in Parameter Design
AUTHORS:
Julio Romero, Scott H. Murray
KEYWORDS:
Experimental Designs, Orthogonal Arrays, Combinatorics, Parameter Design, Backtrack Search
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.3 No.1,
January
28,
2015
ABSTRACT:
This paper describes the construction and
enumeration of mixed orthogonal arrays (MOA) to produce optimal experimental
designs. A MOA is a multiset whose rows are the different combinations of
factor levels, discrete values of the variable under study, having very well
defined features such as symmetry and strength three (all main interactions are
taken in consideration). The applied methodology blends the fields of
combinatorics and group theory by applying the ideas of orbits, stabilizers and
isomorphisms to array generation and enumeration. Integer linear programming
was used in order to exploit the symmetry property of the arrays under study.
The backtrack search algorithm was used to find suitable arrays in the
underlying space of possible solutions. To test the performance of the MOAs, an
engineered system was used as a case study within the stage of parameter
design. The analysis showed how the MOAs were capable of meeting the
fundamental engineering design axioms and principles, creating optimal
experimental designs within the desired context.