混水平均匀设计的构造

我们用离散偏差来度量部分因子设计的均匀性,本文的目的在于寻找一些构造混水平均匀设计的方法,这些方法比文献中已有的方法更简单且计算成本更低.我们得到了离散偏差的一个下界,如果一个U 型设计的离散偏差值达到这个下界,那么该设计是—个均匀设计.我们建立了均匀设计与组合设计理论中一致可分解设计之间的联系.通过一致可分解设计,我们提出了一些构造均匀设计的新方法,同时也给出了许多均匀设计存在的无穷类.     

Construction of optimal supersaturated designs by the packing method

A supersaturated design is essentially a factorial design with the equal occurrence of levels property and no fully aliased factors in which the number of main effects is greater than the number of runs. It has received much recent interest because of its potential in factor screening experiments. A packing design is an important object in combinatorial design theory. In this paper, a strong link between the two apparently unrelated kinds of designs is shown. Several criteria for comparing supersaturated designs are proposed, their properties and connections with other existing criteria are discussed. A combinatorial approach, called the packing method, for constructing optimal supersaturated designs is presented, and properties of the resulting designs are also investigated. Comparisons between the new designs and other existing designs are given, which show that our construction method and the newly constructed designs have good properties.     

Some results on resolvable incomplete block designs

This paper is concerned with the uniformity of a certain kind of resolvable incomplete block (RIB for simplicity) design which is called the PRIB design here. A sufficient and necessary condition is obtained, under which a PRIB design is the most uniform in the sense of a discrete discrepancy measure, and the uniform PRIB design is shown to be connected. A construction method for such designs via a kind of U-type designs is proposed, and an existence result of these designs is given. This method sets up an important bridge between PRIB designs and U-type designs.     

一种构造多水平超饱和设计的新方法

超饱和设计在搜索试验中有重要应用.自上世纪九十年代迄今, 超饱和设计的研究取得了丰硕成果,研究的设计从二水平发展到多水平, 进而到混合水平;构造方法从巧妙的构思到利用组合理论进行系统构造,进而到各种算法的开发; 对于超饱和设计的评优准则也有更深入的认识.本文介绍一种构造多水平超饱和设计的新方法. 这种方法简单易行,很容易构造出具有优良性质的多水平超饱和设计, 有很强的实用性.     

Some properties of double designs in terms of lee discrepancy

Doubling is a simple but powerful method of constructing two-level fractional factorial designs with high resolution. This article studies uniformity in terms of Lee discrepancy of double designs. We give some linkages between the uniformity of double design and the aberration case of the original one under different criteria. Furthermore, some analytic linkages between the generalized wordlength pattern of double design and that of the original one are firstly provided here, which extend the existing findings. The lower bound of Lee discrepancy for double designs is also given.     

低偏差OALHD的构造

本文给出了利用均匀设计和正交表构造低偏差OALH设计的方法，该方法构造的设计既有优良的均匀性具有正交设计的均衡性，一个更重要的优点是可以构造较大样本容量的设计点集，本文同时给出了某些参数的均匀设计表，这些设计优于现有的均匀设计，具有实用价值。     

Construction of Sudoku designs and Sudoku-based uniform designs

In this paper, an easy and effective construction method of Sudoku designs with any order is provided based on the right shift operator. Based on the constructed Sudoku designs, a class of Sudoku-based uniform designs is constructed. Moreover, the properties of the constructed Sudoku designs and Sudoku-based uniform designs are investigated, it is shown that both the constructed Sudoku designs and Sudoku-based uniform designs are uniform designs in terms of discrete discrepancy.     

一种构造三水平因子超饱和设计的准则和算法

在工业统计试验和其他科学试验中,常遇到因子个数多而所允许的试验次数少的情况,这时要用到超饱和设计,以前的文章仅研究了二水平因子的超饱和设计,本文对于三水平因子的超饱和设计提出了一种基于典则相关意义下的优良性准则和构造算法,并给出了试验次数为９和１８可分别安排到２６和３０个因子的三水平超饱和设计表。     

多水平超饱和设计的一类构造方法

过去超饱和设计的研究集中在2水平设计的范围内,Lu and Sun(2000)首次讨论了高于2水平因子的超饱和设计问题,该文提出了用E（d^2)作为构造超饱和设计的准则,并给出了E（d^2)最优的一些设计,本文讨论了以给定的Max(d^2)为前提构造超饱和设计的方法,并给出了一些三水平和四水平的超饱和设计。     

Centered -discrepancy of random sampling and Latin hypercube design, and construction of uniform designs

In this paper properties and construction of designs under a centered version of the -discrepancy are analyzed. The theoretic expectation and variance of this discrepancy are derived for random designs and Latin hypercube designs. The expectation and variance of Latin hypercube designs are significantly lower than that of random designs. While in dimension one the unique uniform design is also a set of equidistant points, low-discrepancy designs in higher dimension have to be generated by explicit optimization. Optimization is performed using the threshold accepting heuristic which produces low discrepancy designs compared to theoretic expectation and variance.