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This paper describes the construction andenumeration of mixed orthogonal arrays MOA to produce optimal experimentaldesigns. A MOA is a multiset whose rows are the different combinations offactor levels, discrete values of the variable under study, having very welldefined features such as symmetry and strength three all main interactions aretaken in consideration. The applied methodology blends the fields ofcombinatorics and group theory by applying the ideas of orbits, stabilizers andisomorphisms to array generation and enumeration. Integer linear programmingwas used in order to exploit the symmetry property of the arrays under study.The backtrack search algorithm was used to find suitable arrays in theunderlying space of possible solutions. To test the performance of the MOAs, anengineered system was used as a case study within the stage of parameterdesign. The analysis showed how the MOAs were capable of meeting thefundamental engineering design axioms and principles, creating optimalexperimental designs within the desired context.

KEYWORDS

Experimental Designs, Orthogonal Arrays, Combinatorics, Parameter Design, Backtrack Search

Cite this paper

Romero, J. and Murray, S. 2015 Enumeration of Strength Three Orthogonal Arrays and Their Implementation in Parameter Design. Journal of Applied Mathematics and Physics, 3, 38-45. doi: 10.4236-jamp.2015.31006.





Autor: Julio Romero, Scott H. Murray

Fuente: http://www.scirp.org/



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