This thesis considers the construction of orthogonal arrays and nearly orthogonal arrays with mixed levels. In Chapter 2, a general approach for constructing asymmetrical orthogonal arrays (or orthogonal arrays with mixed levels) is proposed. This approach combines three methods. First, we construct an asymmetrical orthogonal array as the generalized Kronecker sum of an asymmetrical orthogonal array and some difference matrices. Second, we add columns consisting of copies of another asymmetrical orthogonal array to the array in the first step. Finally, we exploit the relations among columns of the constructed array and use the method of replacement to obtain other arrays. By using this approach, many existing classes of arrays and numerous new classes of arrays can be constructed in a simple and unified manner.; In Chapter 3, we consider the construction of nearly orthogonal arrays with small run sizes. These nearly orthogonal arrays are constructed by adding columns to some orthogonal arrays so that only a few pairs of columns are not orthogonal. The resulting arrays can accommodate more factors than can orthogonal arrays with the same run sizes. Thus by slightly relaxing the orthogonality requirement, we are able to obtain wider choices of arrays. The intelligent search used in constructing such arrays can also be applied to construct other nearly orthogonal arrays.; The constructed arrays have rich applications in experimental design, quality improvement and inference from the complex survey samples.
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