In this article, we consider the characterization problem in design theory. The objective is to characterize minimum projection uniformity for two-level designs in terms of their complementary designs. Here, the compl...In this article, we consider the characterization problem in design theory. The objective is to characterize minimum projection uniformity for two-level designs in terms of their complementary designs. Here, the complementary design means a design in which all the Hamming distances of any two runs are the same, which generalizes the concept of a pair of complementary designs in the literature. Based on relationships of the uniformity pattern between a pair of complementary designs, we propose a minimum projection uniformity （MPU） rule to assess and compare two-level factorials.展开更多
We study the complementary design problem, which is to express the uniformity pattern of a q-level design in terms of that of its complementary design. Here, a pair of complementary designs form a design in which all ...We study the complementary design problem, which is to express the uniformity pattern of a q-level design in terms of that of its complementary design. Here, a pair of complementary designs form a design in which all the Hamming distances of any two distinct runs are the same, and the uniformity pattern proposed by H. Qin, Z. Wang, and K. Chatterjee [J. Statist. Plann. Inference, 2012, 142： 1170-11771 comes from discrete discrepancy for q-level designs. Based on relationships of the uniformity pattern between a pair of complementary designs, we propose a minimum projection uniformity rule to assess and compare q-level factorials.展开更多
Fixed size without replacement sampling designs with probability functions that are linear or quadratic functions of the sampling indicators are defined and studied. Generality, simplicity, remarkable properties, and ...Fixed size without replacement sampling designs with probability functions that are linear or quadratic functions of the sampling indicators are defined and studied. Generality, simplicity, remarkable properties, and also somewhat restricted flexibility characterize these designs. It is shown that the families of linear and quadratic designs are closed with respect to sample complements and with respect to conditioning on sampling outcomes for specific units. Relations between inclusion probabilities and parameters of the probability functions are derived and sampling procedures are given.展开更多
Supersaturated designs （SSDs） have been widely used in factor screening experiments. The present paper aims to prove that the maximal balanced designs are a kind of special optimal SSDs under the E（fNOD） criterion...Supersaturated designs （SSDs） have been widely used in factor screening experiments. The present paper aims to prove that the maximal balanced designs are a kind of special optimal SSDs under the E（fNOD） criterion. We also propose a new method, called the complementary design method, for constructing E（fNoD） optimal SSDs. The basic principle of this method is that for any existing E（fNOD） optimal SSD whose E（fNOD） value reaches its lower bound, its complementary design in the corresponding maximal balanced design is also E（fNOD） optimal. This method applies to both symmetrical and asymmetrical （mixed-level） cases. It provides a convenient and efl：icient way to construct many new designs with relatively large numbers of factors. Some newly constructed designs are given as examples.展开更多
Starting from the definition of Basic Complementary Coding (CC) Pairs, this paper presents a scheme of designing CC signals for practical applications. In comparison with the scheme based directly on the definition of...Starting from the definition of Basic Complementary Coding (CC) Pairs, this paper presents a scheme of designing CC signals for practical applications. In comparison with the scheme based directly on the definition of CC pairs, the present scheme can speed up the operation process for finding CC pairs by 24 × 2N/2 times when the number of coding units N>4.展开更多
基金supported by the NSF of China (10671080)NCET (06-672)the Key Project of Chinese Ministry of Education (105119)
文摘In this article, we consider the characterization problem in design theory. The objective is to characterize minimum projection uniformity for two-level designs in terms of their complementary designs. Here, the complementary design means a design in which all the Hamming distances of any two runs are the same, which generalizes the concept of a pair of complementary designs in the literature. Based on relationships of the uniformity pattern between a pair of complementary designs, we propose a minimum projection uniformity （MPU） rule to assess and compare two-level factorials.
基金Acknowledgements The authors greatly appreciate helpful suggestions of the referees that greatly improved the paper. This work was supported in part by the National Natural Science Foundation of China （Grant Nos. 11271147, 11401596）.
文摘We study the complementary design problem, which is to express the uniformity pattern of a q-level design in terms of that of its complementary design. Here, a pair of complementary designs form a design in which all the Hamming distances of any two distinct runs are the same, and the uniformity pattern proposed by H. Qin, Z. Wang, and K. Chatterjee [J. Statist. Plann. Inference, 2012, 142： 1170-11771 comes from discrete discrepancy for q-level designs. Based on relationships of the uniformity pattern between a pair of complementary designs, we propose a minimum projection uniformity rule to assess and compare q-level factorials.
基金supported by the Estonian Science Foundation grant 8789
文摘Fixed size without replacement sampling designs with probability functions that are linear or quadratic functions of the sampling indicators are defined and studied. Generality, simplicity, remarkable properties, and also somewhat restricted flexibility characterize these designs. It is shown that the families of linear and quadratic designs are closed with respect to sample complements and with respect to conditioning on sampling outcomes for specific units. Relations between inclusion probabilities and parameters of the probability functions are derived and sampling procedures are given.
基金Supported by the National Natural Science Foundation of China (Nos. 10971107 and 11271205)the "131" Talents Program of Tianjin+1 种基金the Fundamental Research Funds for the Central Universities (No. 65030011)the Doctor Foundation of Tianjin Normal University (No. 52XB1205)
文摘Supersaturated designs （SSDs） have been widely used in factor screening experiments. The present paper aims to prove that the maximal balanced designs are a kind of special optimal SSDs under the E（fNOD） criterion. We also propose a new method, called the complementary design method, for constructing E（fNoD） optimal SSDs. The basic principle of this method is that for any existing E（fNOD） optimal SSD whose E（fNOD） value reaches its lower bound, its complementary design in the corresponding maximal balanced design is also E（fNOD） optimal. This method applies to both symmetrical and asymmetrical （mixed-level） cases. It provides a convenient and efl：icient way to construct many new designs with relatively large numbers of factors. Some newly constructed designs are given as examples.
基金The project supported by The National Natural Science Foundation of China
文摘Starting from the definition of Basic Complementary Coding (CC) Pairs, this paper presents a scheme of designing CC signals for practical applications. In comparison with the scheme based directly on the definition of CC pairs, the present scheme can speed up the operation process for finding CC pairs by 24 × 2N/2 times when the number of coding units N>4.
