一般最小低阶混杂设计的统计性质

本文旨在研究满足N/4+2≤n≤5N/16的GMC 2n-m设计的统计性质(N=2n-m),首先通过研究这些设计别名关系来讨论其估计能力,然后提出了一种新的理论方法用以得到这些设计的混杂信息,最后给出了可供实际使用的试验表格.     

用数理统计方法讨论核桃剥壳取仁机理

吴斌方等．用数理统计方法讨论核桃剥壳取仁机理．数理统计与管理，１９９７，１６（４），１６～１８本文以大量实验数据为基础，应用数理统计和方差分析的方法，论证了二对集中力滚动挤压有利于绵核桃剥壳取仁，从而为设计绵核桃剥壳取仁机提供了理论基础。     

一类k步k＋1阶SDBDF型混杂法

本文在ＳＤＢＤＦ方法的基础上构造了一类ｋ步ｋ＋１阶的ＳＤＢＤＦ型混杂法，讨论了该方法的稳定性质，证明了ｋ＝１，２，３时，方法是Ａ稳定的，ｋ＝４～１０时方法是ｓｔｉｆ稳定的，同ＢＤＦ型和Ａｄａｍｓ型混杂法相比，该方法的ｓｔｉｆ稳定阶大有提高，这两类方法的ｓｔｉｆ稳定阶只能分别达到８阶和９阶〔２，３，５〕．在实现Ｎｅｗｔｏｎ迭代计算时，我们的方法要优于原ＳＤＢＤＦ方法，因此对于求解ｓｔｉｆ问题，我们的这类方法具有一定的优势，最后给出了数值实例     

某些包含最多纯净两因子交互效应2m-(m-k)Ⅲ设计的一种构造方法

本文给出了构造包含最多纯净两因子交互效应2m-(m-k)Ⅲ设计的一种方法.对于某些设计参数m和k,验证了所构造的设计包含纯净两因子交互效应的数量多于Tang et al.(2002)所构造的设计.并且所构造的设计都给出了格子点表示.     

几个对参数设计有用的正交表

本文给出对参数设计有用的几个正交表Ｌ′１６（２１２），Ｌ′１６（２１４），Ｌ３６（２１１×３１２），Ｌ１０８（３４９），Ｌ１０８（２３×３４９），Ｌ１０８（２１１×３４８）和Ｌ１０８（２３５×３３６）这些正交表不包含交互作用列，适合于参数设计使用。本文还将证明Ｌ４５（３２２）和Ｌ６３（３３１）的不可能性。     

利用2Ⅳ^m-p设计的纯净两因子交互效应个数判断低阶混杂

根据纯净两因子交互效应的数量证明某些2Ⅳ^m-p设计在一定条件下具有弱最小低阶混杂，并且给出了一组既具有弱最小低阶混杂又包含最大数量纯净两因子交互效应的2Ⅳ^m-p设计．     

正交设计的最新发展和应用-回归分析在正交设计的应用

正交设计有许多新发展,本系列讲座介绍其中的一些便于应用的结果,共有四部份：回归分析在正交设计中的应用,均匀正交设计,正交设计的Ｄ－最优性,以及正交设计的投影性质。本讲强调回归分析用于正交设计的建模、估计、减少参数数目方面的应用     

某些包含最多纯净两因子交互效应2_Ⅲ~(m-(m-k))设计的一种构造方法(英文)

本文给出了构造包含最多纯净两因子交互效应2Ⅲm-(m-k)设计的一种方法.对于某些设计参数m和k,验证了所构造的设计包含纯净两因子交互效应的数量多于Tang et al.(2002)所构造的设计.并且所构造的设计都给出了格子点表示.     

三水平超饱和设计的构造及性质

超饱和设计是一类重要的部分因析设计,因其在因子筛选试验中有重要作用而受到广泛关注.文章基于水平置换方式并对设计进行倍扩的方法,实现由规模较小且性质优良的设计来构造超饱和设计,并分别在E(f_NOD),广义最小低价混杂和最小矩混杂等准则下讨论了所构造的超饱和设计的优良性质.最后,数值例子的结果验证了文章的理论结果.     

某些包含最多纯净两因子交互效应$2_{\rm{III}}^{m-(m-k)}$设计的一种构造方法

本文给出了构造包含最多纯净两因子交互效应$2_{\text{III}}^{m-(m-k)}$设计的一种方法.对于某些设计参数$m$和$k$, 验证了所构造的设计包含纯净两因子交互效应的数量多于Tang et al. (2002)所构造的设计. 并且所构造的设计都给出了格子点表示.     

Quasi-symmetric 2-(28, 12, 11) designs with an automorphism of order 7

All quasi-symmetric 2-(28, 12, 11) designs with an automorphism of order 7 without fixed points or blocks are enumerated. Up to isomorphism, there are exactly 246 such designs. All but four of these designs are embeddable as derived designs in symmetric 2-(64, 28, 12) designs, producing in this way at least 8784 nonisomorphic symmetric 2-(64, 28, 12) designs. The remaining four 2-(28, 12, 11) designs are the first known examples of nonembeddable quasi-symmetric quasi-derived designs. These symmetric 2-(64, 28, 12) designs also produce at least 8784 nonisomorphic quasi-symmetric 2-(36, 16, 12) designs with intersection numbers 6 and 8, including the first known examples of quasi-symmetric 2-(36, 16, 12) designs with a trivial automorphism group. © 1998 John Wiley & Sons, Inc. J Combin Designs 6: 213–223, 1998     

Some third-order rotatable designs in three dimensions

Summary Some new third-order rotatable designs in three dimensions are derived from some of the available third-order rotatable designs in two dimensions. When these designs are used the results of the experiments performed according to the two-dimentional designs need not be discarded. Some of these designs may be performed sequentially in all three factors, starting with a one-dimensional design. Further, these third-order rotatable designs require a smaller number of points than most of the available three-dimensional third-order rotatable designs.     

The existence of symmetric block designs with parameters (41, 16, 6) and (66, 26, 10)

In [1, 2] it is indicated that the existence of block designs with parameters (41, 16, 6) and (66, 26, 10) is still unknown. The purpose of this paper is to prove the existence of block designs with these parameters. The idea for the construction of these block designs is to assume that they admit certain automorphism group.     

An effective algorithm for generation of factorial designs with generalized minimum aberration

Fractional factorial designs are popular and widely used for industrial experiments. Generalized minimum aberration is an important criterion recently proposed for both regular and non-regular designs. This paper provides a formal optimization treatment on optimal designs with generalized minimum aberration. New lower bounds and optimality results are developed for resolution-III designs. Based on these results, an effective computer search algorithm is provided for sub-design selection, and new optimal designs are reported.     

A new family of covariate-adjusted response adaptive designs and their properties

It is often important to incorporate covariate information in the design of clinical trials. In literature there are many designs of using stratification and covariate-adaptive randomization to balance certain known covariate. Recently, some covariate-adjusted response-adaptive （CARA） designs have been proposed and their asymptotic properties have been studied （Ann. Statist. 2007）. However, these CARA designs usually have high variabilities. In this paper, a new family of covariate-adjusted response-adaptive （CARA） designs is presented. It is shown that the new designs have less variables and therefore are more efficient.     

A fresh look at effect aliasing and interactions: some new wine in old bottles

Interactions and effect aliasing are among the fundamental concepts in experimental design. In this paper, some new insights and approaches are provided on these subjects. In the literature, the “de-aliasing” of aliased effects is deemed to be impossible. We argue that this “impossibility” can indeed be resolved by employing a new approach which consists of reparametrization of effects and exploitation of effect non-orthogonality. This approach is successfully applied to three classes of designs: regular and nonregular two-level fractional factorial designs, and three-level fractional factorial designs. For reparametrization, the notion of conditional main effects (cme’s) is employed for two-level regular designs, while the linear-quadratic system is used for three-level designs. For nonregular two-level designs, reparametrization is not needed because the partial aliasing of their effects already induces non-orthogonality. The approach can be extended to general observational data by using a new bi-level variable selection technique based on the cme’s. A historical recollection is given on how these ideas were discovered.     

Construction of uniform designs without replications

A uniform design scatters its design points evenly on the experimental domain according to some discrepancy measure. In this paper all the design points of a full factorial design can be split into two subdesigns. One is called the complementary design of the other. The complementary design theories of characterizing one design through the other under the four commonly used discrepancy measures are investigated. Based on these complementary design theories, some general rules for searching uniform designs through their complementary designs are proposed. An efficient method to check if a design has repeated points is introduced and a modified threshold-accepting algorithm is proposed to search uniform or nearly uniform designs without replications. The new algorithm is shown to be more efficient by comparing with other existing methods. Many new uniform or nearly uniform designs without replications are tabulated and compared.     

A class of saturated row-column designs

A new class of saturated, binary row-column designs is proposed. It is shown that these designs are treatment connected in the sense that these permit the estimability of all contrasts among treatment effects.     

投影均匀分片拉丁超立方体设计

空间填充设计是有效的计算机试验设计,比如均匀设计、最大最小距离拉丁超立方体设计等.虽然这些设计在整个试验空间中有较好的均匀性,但其低维投影均匀性可能并不理想.对于因子是定量的计算机试验,已有文献构造了诸如最大投影设计、均匀投影设计等相适应的设计;而对于同时含有定性因子和定量因子的计算机试验,尚未有投影均匀设计的相关文献.文章提出了综合投影均匀准则,利用门限接受算法构造了投影均匀的分片拉丁超立方体设计.在新构造设计中,整体设计与每一片设计均具有良好的投影均匀性.模拟结果显示,与随机分片拉丁超立方体设计相比,利用新构造设计进行试验而拟合的高斯过程模型具有更小的均方根预测误差.     

The application of invariant theory to the existence of quasi-symmetric designs

Gleason and Mallows and Sloane characterized the weight enumerators of maximal self-orthogonal codes with all weights divisible by 4. We apply these results to obtain a new necessary condition for the existence of 2 − (v, k, λ) designs where the intersection numbers s₁…,s_n satisfy s₁ ≡ s₂ ≡ … ≡ s_n (mod 2). Non-existence of quasi-symmetric 2−(21, 18, 14), 2−(21, 9, 12), and 2−(35, 7, 3) designs follows directly from the theorem. We also eliminate quasi-symmetric 2−(33, 9, 6) designs. We prove that the blocks of quasi-symmetric 2−(19, 9, 16), 2−(20, 10, 18), 2-(20,8, 14), and 2−(22, 8, 12) designs are obtained from octads and dodecads in the [24, 12] Golay code. Finally we eliminate quasi-symmetric 2−(19,9, 16) and 2-(22, 8, 12) designs.