Orthogonal arrays (OAs), mixed level or fixed level (asymmetric or symmetric), are useful in the design of various experiments. They are also a fundamental tool in the construction of various combinatorial configurati...Orthogonal arrays (OAs), mixed level or fixed level (asymmetric or symmetric), are useful in the design of various experiments. They are also a fundamental tool in the construction of various combinatorial configurations. In this paper, we establish a general "expansive replacement method" for constructing mixedlevel OAs of an arbitrary strength. As a consequence, a positive answer to the question about orthogonal arrays posed by Hedayat, Sloane and Stufken is given. Some series of mixed level OAs of strength ≥3 are produced.展开更多
The objective of this paper is to discuss the issue of the projection uniformity of asymmetric fractional factorials.On the basis of Lee discrepancy,the authors define the projection Lee discrepancy to measure the uni...The objective of this paper is to discuss the issue of the projection uniformity of asymmetric fractional factorials.On the basis of Lee discrepancy,the authors define the projection Lee discrepancy to measure the uniformity for low-dimensional projection designs.Moreover,the concepts of uniformity pattern and minimum projection uniformity criterion are proposed,which can be used to assess and compare two and three mixed levels factorials.Statistical justification of uniformity pattern is also investigated.展开更多
Cohabiting with so many neighbors that form a unique surrounding area, China has always had complex and changeable neighborhood relationships. To understand China's relations with its neighboring countries (or neigh...Cohabiting with so many neighbors that form a unique surrounding area, China has always had complex and changeable neighborhood relationships. To understand China's relations with its neighboring countries (or neighborhood relations), one may take the following four different perspectives, namely, geography, relationship, interests and competition. Different perspectives will give rise to different characteristics and meanings of the relationship. The most direct and profound meaning of geography is that China and its neighbors are closely connected and co-habit in the same area, which is a fact that could never be changed. Relationship contains bilateral and multilateral relations as well as immediate and long-term relations, which constitute complex, multi-layer and mixed levels of relations and network. Interests are various and varied; but no matter how different they may be, they are direct and difficult to give up. As to competition, not only it exists between China and its neighbors but there are also involvement and scheming by outside forces. No other country in the world has so complex and complicated neighborhood relations as China does.展开更多
Mukerjee and Wu(2001) employed projective geometry theory to find the wordlength pattern of a regular mixed factorial design in terms of its complementary set, but only for the numbers of words of length 3 or 4. In ...Mukerjee and Wu(2001) employed projective geometry theory to find the wordlength pattern of a regular mixed factorial design in terms of its complementary set, but only for the numbers of words of length 3 or 4. In this paper, by introducing a concept of consulting design and based on the connection between factorial design theory and coding theory, we obtain some combinatorial identities that relate the wordlength pattern of a regular mixed-level (2^r)2^n factorial design to that of its consulting design. Consequently, a general rule for identifying minimum aberration (2^r)2^n factorial designs through their consulting designs is established. It is an improvement and generalization of the related result in Mukerjee and Wu(2001).展开更多
基金supported by National Natural Science Foundation of China (Grant Nos.11271280 and 10831002)
文摘Orthogonal arrays (OAs), mixed level or fixed level (asymmetric or symmetric), are useful in the design of various experiments. They are also a fundamental tool in the construction of various combinatorial configurations. In this paper, we establish a general "expansive replacement method" for constructing mixedlevel OAs of an arbitrary strength. As a consequence, a positive answer to the question about orthogonal arrays posed by Hedayat, Sloane and Stufken is given. Some series of mixed level OAs of strength ≥3 are produced.
基金supported by the National Natural Science Foundations of China under Grant Nos.11271147 and 11401596
文摘The objective of this paper is to discuss the issue of the projection uniformity of asymmetric fractional factorials.On the basis of Lee discrepancy,the authors define the projection Lee discrepancy to measure the uniformity for low-dimensional projection designs.Moreover,the concepts of uniformity pattern and minimum projection uniformity criterion are proposed,which can be used to assess and compare two and three mixed levels factorials.Statistical justification of uniformity pattern is also investigated.
文摘Cohabiting with so many neighbors that form a unique surrounding area, China has always had complex and changeable neighborhood relationships. To understand China's relations with its neighboring countries (or neighborhood relations), one may take the following four different perspectives, namely, geography, relationship, interests and competition. Different perspectives will give rise to different characteristics and meanings of the relationship. The most direct and profound meaning of geography is that China and its neighbors are closely connected and co-habit in the same area, which is a fact that could never be changed. Relationship contains bilateral and multilateral relations as well as immediate and long-term relations, which constitute complex, multi-layer and mixed levels of relations and network. Interests are various and varied; but no matter how different they may be, they are direct and difficult to give up. As to competition, not only it exists between China and its neighbors but there are also involvement and scheming by outside forces. No other country in the world has so complex and complicated neighborhood relations as China does.
文摘Mukerjee and Wu(2001) employed projective geometry theory to find the wordlength pattern of a regular mixed factorial design in terms of its complementary set, but only for the numbers of words of length 3 or 4. In this paper, by introducing a concept of consulting design and based on the connection between factorial design theory and coding theory, we obtain some combinatorial identities that relate the wordlength pattern of a regular mixed-level (2^r)2^n factorial design to that of its consulting design. Consequently, a general rule for identifying minimum aberration (2^r)2^n factorial designs through their consulting designs is established. It is an improvement and generalization of the related result in Mukerjee and Wu(2001).