On The Construction Of Asymmetric Orthogonal Arrays

The orthogonal arrays are essential in the field of experimental designs,so it is very important to study the method of its construction.Compared with symmetric orthogonal arrays,asymmet-ric orthogonal arrays are more flexible and practical,which makes people start the research of construction methods.Asymmetric orthogonal arrays have also been found very useful in indus-trial experimentation for quality control and quality improvement.Asymmetric orthogonal arrays introduced by Rao[22]have received considerable attention in recent years.Construction of asym-metric orthogonal arrays of strength two has been widely studied.Relatively less is known on the construction of asymmetric orthogonal arrays of strength larger than two.A general method of construction of asymmetric orthogonal arrays was proposed by Suen et al.[24].Using this method and some modifications thereof,we construct some more families of asymmetric orthogonal arrays of strength greater than two.The details are as follow:Chapter 1 is to introduce the background and current situation of asymmetric orthogonal arrays.Chapter 2 is to introduce some related basic concepts and main lemma.And we apply the method of Suen et al.[24]to obtain some more asymmetric orthogonal arrays of strength three.At the end of this chapter,we also give an alternative method of construction of a family of asymmetric orthogonal arrays of strength four,which appears to be more direct than that of Suen and Dey[25].Chapter 3 is to present a new method of construction of asymmetric orthogonal arrays.Us-ing this method,we construct some more families of asymmetric orthogonal arrays of arbitrary strength.And then we illustrate this through examples.We also construct some tight asymmetric orthogonal arrays at the end of this chapter.Chapter 4 is to summarize the main content of this paper and put forward some suggestions and a few unsolved problems.