Enumeration of strength three orthogonal arrays and their application in parameter design

Abstract

Experimental design is an important and broadly applied area of statistics. The expansion of this field to the areas of industrial processes and engineered systems has boosted the study of designs constructed through combinatorial techniques such as Hadamard matrices, Latin squares, and orthogonal arrays. The last is the basis of our research. Basically, an orthogonal array is a sequence of different combinations of factor levels (discrete values of the variable under study), having well-defined orthogonal properties. The methodology we use blends the fields of engineering, statistics, combinatorics, group theory, and backtrack search. The purpose of this research is the construction and enumeration of orthogonal arrays and their implementation in engineering parameter design. We now outline the outcomes of this thesis: We enumerate orthogonal arrays and the corresponding size of the automorphism groups, some of which are not yet listed in the current literature. We construct orthogonal arrays by using a consistent technique to reproduce many different design types. We develop a more flexible and customisable technique to deal with robust design. We implement a powerful approach to merge parameter design and probabilistic design. Finally we create a novel approach to implement orthogonal arrays when modelling servomotors in a robotic-arm design.

Date of Award	2017
Original language	English
Supervisor	Scott Murray (Supervisor), Shuangzhe LIU (Supervisor) & Judith Ascione (Supervisor)