Enumeration of Strength Three Orthogonal Arrays and Their Implementation in Parameter Design

Julio Romero, Scott H. Murray

Faculty of Education, Science, Technology and Mathematics, University of Canberra, Canberra, Australia.

DOI: 10.4236/jamp.2015.31006                

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.

Keywords

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

Conflicts of Interest

The authors declare no conflicts of interest.

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