Book ChapterDOI
Uniformity in Fractional Factorials
Kai-Tai Fang,Chang-Xing Ma,Rahul Mukerjee +2 more
- pp 232-241
Reads0
Chats0
TLDR
In this paper, the authors studied the role of uniformity in fractional factorial designs and derived results connecting orthogonality, aberration, and uniformity for fractions of two-or three-level factorials.Abstract:
The issue of uniformity is crucial in quasi-Monte Carlo methods and in the design of computer experiments. In this paper we study the role of uniformity in fractional factorial designs. For fractions of two- or three-level factorials, we derive results connecting orthogonality, aberration and uniformity and show that these criteria agree quite well. This provides further justification for the criteria of orthogonality or minimum aberration in terms of uniformity. Our results refer to several natural measures of uniformity and we consider both regular and nonregular fractions. The theory developed here has the potential of significantly reducing the complexity of computation for searching for minimum aberration designs.read more
Citations
More filters
Book ChapterDOI
Ch. 4. Uniform experimental designs and their applications in industry
Kai-Tai Fang,Dennis K.J. Lin +1 more
TL;DR: In this paper, the authors introduce the theory and method of the uniform design and related data analysis and modelling methods, and apply it to industry and other areas, including space filling.
Journal ArticleDOI
Uniform designs limit aliasing
Fred J. Hickernell,Min-Qian Liu +1 more
TL;DR: In this article, it is shown that uniform designs limit the effects of aliasing to yield reasonable efficiency and robustness together, while robust experimental designs guard against inaccurate estimates caused by model misspecification.
Journal ArticleDOI
Discrete discrepancy in factorial designs
Hong Qin,Hong Qin,Kai-Tai Fang +2 more
TL;DR: In this article, the authors give linkages among uniformity measured by the discrete discrepancy, generalized minimum aberration, minimum moment aberration and uniformity measure by the centered L2-discrepancy/the wrap-around L2 discrepancy.
Journal ArticleDOI
A note on construction of nearly uniform designs with large number of runs
Kai-Tai Fang,Hong Qin,Hong Qin +2 more
TL;DR: In this paper, the authors proposed a way to construct nearly uniform designs with large number of runs by collapsing two uniform designs in the sense of low-discrepancy, which is the product of the two numbers of runs of both original designs.
Journal ArticleDOI
Uniformity pattern and related criteria for two-level factorials
Kai-Tai Fang,Hong Qin,Hong Qin +2 more
TL;DR: In this article, the study of projection properties of two-level factorials in view of geometry is reported, and a new concept of uniformity pattern is defined based on this new concept.
References
More filters
Book
Random number generation and quasi-Monte Carlo methods
TL;DR: This chapter discusses Monte Carlo methods and Quasi-Monte Carlo methods for optimization, which are used for numerical integration, and their applications in random numbers and pseudorandom numbers.
Journal ArticleDOI
Uniform Design: Theory and Application
TL;DR: It is shown that UD's have many desirable properties for a wide variety of applications and the global optimization algorithm, threshold accepting, is used to generate UD's with low discrepancy.
Journal ArticleDOI
A generalized discrepancy and quadrature error bound
TL;DR: An error bound for multidimensional quadrature is derived that includes the Koksma-Hlawka inequality as a special case and includes as special cases the L p -star discrepancy and P α that arises in the study of lattice rules.
Journal ArticleDOI
Number-theoretic methods in statistics
Kai-Tang Fang,Yuan Wang +1 more
TL;DR: In this paper, a number-theoretic method for numerical evaluation of multiple integral in statistics is presented, and its applications in statistics are discussed. But this method is not suitable for the analysis of multivariate distributions.
Book
Applications of number theory to numerical analysis
Lo-keng Hua,Yuan Wang +1 more
TL;DR: In this paper, the authors present an algebraic number field model for the problem of finding a rational approximation of a polynomial in an integral basis with respect to an integer number field.