首页 | 本学科首页   官方微博 | 高级检索  
相似文献
 共查询到20条相似文献,搜索用时 31 毫秒
1.
This paper presents the trace of the covariance matrix of the estimates of effects based on a fractional 2m factorial (2m-FF) design T of resolution V for the following two cases: One is the case where T is constructed by adding some restricted assemblies to an orthogonal array. The other is one where T is constructed by removing some restricted assemblies from an orthogonal array of index unity. In the class of 2m-FF designs of resolution V considered here, optimal designs with respect to the trace criterion, i.e. A-optimal, are presented for m = 4, 5, and 6 and for a range of practical values of N (the total number of assemblies). Some of them are better than the corresponding A-optimal designs in the class of balanced fractional 2m factorial designs of resolution V obtained by Srivastava and Chopra (1971b) in such a sense that the trace of the covariance matrix of the estimates is small.  相似文献   

2.
In this paper we study the sensitivity of the optimum balanced resolution V plans for 2m factorials, to outliers, using the measure suggested by Box and Drapper (1975). We observe that the designs are robust, i.e., have low sensitivity.  相似文献   

3.
We consider a search design for the 2m type such that at most knonnegative effects can be searched among (l+1)-factor interactions and estimated along with the effects up to l- factor interactions, provided (l+1)-factor and higher order interactions are negligible except for the k effects. We investigate some properties of a search design which is yielded by a balanced 2m design of resolution 2l+1 derived from a balanced array of strength 2(l+1). A necessary and sufficient condition for the balanced design of resolution 2l+1 to be a search design for k=1 is given. Optimal search designs for k=1 in the class of the balanced 2m designs of resolution V (l=2), with respect to the AD-optimality criterion given by Srivastava (1977), with N assemblies are also presented, where the range of (m,N) is (m=6; 28≤N≤41), (m=7; 35≤N≤63) and (m=8; 44≤N≤74).  相似文献   

4.
The norm 6A6 = {tr(A′A)}12 of the alias matrix A of a design can be used as a measure for selecting a design. In this paper, an explicit expression for 6A6 will be given for a balanced fractional 2m factorial design of resolution 2l + 1 which obtained from a simple array with parameters (m; λ0, λ1,…, λm). This array is identical with a balanced array of strength m, m constraints and index set {λ0, λ1,…, λm}. In the class of the designs of resolution V (l = 2) obtained from S-arrays, ones which minimize 6A6 will be presented for any fixed N assemblies satisfying (i) m = 4, 11 ? N ? 16, (ii) m = 5, 16 ? N ? 32, and (iii) m = 6, 22 ? N ? 40.  相似文献   

5.
The purpose of this article is to introduce a new class of extended E(s2)-optimal two level supersaturated designs obtained by adding runs to an existing E(s2)-optimal two level supersaturated design. The extended design is a union of two optimal SSDs belonging to different classes. New lower bound to E(s2) has been obtained for the extended supersaturated designs. Some examples and a small catalogue of E(s2)-optimal SSDs are also included.  相似文献   

6.
A connection between a balanced fractional 2m factorial design of resolution 2l + 1 and a balanced array of strength 2l with index set {μ0, μ1,…, μ2l} was established by Yamamoto, Shirakura and Kuwada (1975). The main purpose of this paper is to give a connection between a balanced fractional 3m factorial design of resolution V and a balanced array of strength 4, size N, m constraints, 3 levels and index set {λl0l1l2}.  相似文献   

7.
An explicit expression for the characteristic polynomial of the information matrix MT of a balanced fractional 3m factorial (3m-BFF) design T of resolution V is obtained by utilizing the algebraic structure of the underlying multidimentional relationship. Also by using of the multidimensional relationship algebra, the trace and the determinant of the covariance matrix of the estimates of effects are derived.  相似文献   

8.
We prove that if pr and pr ? 1 are both prime powers then there is a generalized Hadamard matrix of order pr(pr ? 1) with elements from the elementary abelian group Zp x?x Zp. This result was motivated by results of Rajkundia on BIBD's. This result is then used to produce pr ? 1 mutually orthogonal F-squares F(pr(pr ? 1); pr ? 1).  相似文献   

9.
In this paper, we discuss resolution III plans for 2m factorial experiments which have an additional property. We relax the classical assumption that all the interactions are negligible by assuming that (at most) one of them may be nonnegligible. Which interaction is nonnegligible is unknown. We discuss designs which allow the search and estimation of this interaction, along with the estimation of the general mean and the main effects as in the classical resolution III designs.  相似文献   

10.
In this paper, we obtain search designs with reasonably small number of treatments which permit the estimation of the general mean and main effects and search of one more unknown possible nonzero effect among two and three factor interactions in 2m factorial experiments, 3 ? m ? 8.  相似文献   

11.
We consider the Gauss-Markoff model (Y,X0β,σ2V) and provide solutions to the following problem: What is the class of all models (Y,Xβ,σ2V) such that a specific linear representation/some linear representation/every linear representation of the BLUE of every estimable parametric functional p'β under (Y,X0β,σ2V) is (a) an unbiased estimator, (b) a BLUE, (c) a linear minimum bias estimator and (d) best linear minimum bias estimator of p'β under (Y,Xβ,σ2V)? We also analyse the above problems, when attention is restricted to a subclass of estimable parametric functionals.  相似文献   

12.
An explicit expression for the characteristic polynomial of the information matrix for a balanced fractional sm factorial design of resolution Vp, q (in particular, when p = q = s − 1, of resolution V) is obtained by utilizing the decomposition of a multidimensional relationship algebra into its four two-sided ideals. Furthermore, by use of the algebraic structure of the underlying multidimensional relationship, the trace and the determinant of the covariance matrix of the estimates of effects to be interest are derived.  相似文献   

13.
A linear model with one treatment at V levels and first order regression on K continuous covariates with values on a K-cube is considered. We restrict our attention to classes of designs d for which the number of observations N to be taken is a multiple of V, i.e. N = V × R with R ≥2, and each treatment level is observed R times. Among these designs, called here equireplicated, there is a subclass characterized by the following: the allocation matrix of each treatment level (for short, allocation matrix) is obtained through cyclic permutation of the columns of the allocation matrix of the first treatment level. We call these designs cyclic. Besides having easy representation, the most efficient cyclic designs are often D-optimal in the class of equireplicated designs. A known upper bound for the determinant of the information matrix M(d) of a design, in the class of equireplicated ones, depends on the congruences of N and V modulo 4. For some combinations of parameter moduli, we give here methods of constructing families of D-optimal cyclic designs. Moreover, for some sets of parameters (N, V,K = V), where the upper bound on ∣M(d)∣ (for that specific combination of moduli) is not attainable, it is also possible to construct highly D-efficient cyclic designs. Finally, for N≤24 and V≤6, computer search was used to determine the most efficient design in the class of cyclic ones. They are presented, together with their respective efficiency in the class of equireplicated designs.  相似文献   

14.
A weighted A-optimality (WA-optimality) criterion is discussed for selecting a fractional 2m factorial design of resolution V. A WA-optimality criterion having one weight may be considered for designs. It is shown that designs derived from orthogonal arrays are WA-optimal for any weight. From a WA-optimal design, a procedure for finding WA-optimal designs for various weights is given. WA-optimal balanced designs are presented for 4 ⩽ m ⩽ 7 and for the values of n assemblies in certain ranges. It is pointed out that designs for m = 7 and for n = 41, 42 given in Chopra and Srivastava (1973a) or in the corrected paper by Chopra et al. (1986), are not A-optimal.  相似文献   

15.
Theorems 5, 6 and 10, and Tables 1–2 in Ghosh (1981) are corrected. These are concerned with search designs which permit the estimation of the general mean and main effects, and allow the search and estimation of one possibly unknown nonzero effect among the two- and three-factor interactions in 2m factorial experiments. Some new results are presented.  相似文献   

16.
Factor screening designs for searching two and three effective factors using the search linear model are discussed. The construction of such factor screening designs involved finding a fraction with small number of treatments of a 2m factorial experiment having the property P2t (no 2t columns are linearly dependent) for t=2 and 3. A ‘Packing Problem’ is introduced in this connection. A complete solution of the problem in one case and partial solutions for the other cases are presented. Many practically useful new designs are listed.  相似文献   

17.
In this paper we consider linear sufficiency and linear completeness in the context of estimating the estimable parametric function KβKβ under the general Gauss–Markov model {y,Xβ2V}{y,Xβ,σ2V}. We give new characterizations for linear sufficiency, and define and characterize linear completeness in a case of estimation of KβKβ. Also, we consider a predictive approach for obtaining the best linear unbiased estimator of KβKβ, and subsequently, we give the linear analogues of the Rao–Blackwell and Lehmann–Scheffé Theorems in the context of estimating KβKβ.  相似文献   

18.
Let GF(s) be the finite field with s elements.(Thus, when s=3, the elements of GF(s) are 0, 1 and 2.)Let A(r×n), of rank r, and ci(i=1,…,f), (r×1), be matrices over GF(s). (Thus, for n=4, r=2, f=2, we could have A=[11100121], c1=[10], c2=[02].) Let Ti (i=1,…,f) be the flat in EG(n, s) consisting of the set of all the sn?r solutions of the equations At=ci, wheret′=(t1,…,tn) is a vector of variables.(Thus, EG(4, 3) consists of the 34=81 points of the form (t1,t2,t3,t4), where t's take the values 0,1,2 (in GF(3)). The number of solutions of the equations At=ci is sn?r, where r=Rank(A), and the set of such solutions is said to form an (n?r)-flat, i.e. a flat of (n?r) dimensions. In our example, both T1 and T2 are 2-flats consisting of 34?2=9 points each. The flats T1,T2,…,Tf are said to be parallel since, clearly, no two of them can have a common point. In the example, the points of T1 are (1000), (0011), (2022), (0102), (2110), (1121), (2201), (1212) and (0220). Also, T2 consists of (0002), (2010), (1021), (2101), (1112), (0120), (1200), (0211) and (2222).) Let T be the fractional design for a sn symmetric factorial experiment obtained by taking T1,T2,…,Tf together. (Thus, in the example, 34=81 treatments of the 34 factorial experiment correspond one-one with the points of EG(4,3), and T will be the design (i.e. a subset of the 81 treatments) consisting of the 18 points of T1 and T2 enumerated above.)In this paper, we lay the foundation of the general theory of such ‘parallel’ types of designs. We define certain functions of A called the alias component matrices, and use these to partition the coefficient matrix X (n×v), occuring in the corresponding linear model, into components X.j(j=0,1,…,g), such that the information matrix X is the direct sum of the X′.jX.j. Here, v is the total number of parameters, which consist of (possibly μ), and a (general) set of (geometric) factorial effects (each carrying (s?1) degrees of freedom as usual). For j≠0, we show that the spectrum of X′.jX.j does not change if we change (in a certain important way) the usual definition of the effects. Assuming that such change has been adopted, we consider the partition of the X.j into the Xij (i=1,…,f). Furthermore, the Xij are in turn partitioned into smaller matrices (which we shall here call the) Xijh. We show that each Xijh can be factored into a product of 3 matrices J, ζ (not depending on i,j, and h) and Q(j,h,i)where both the Kronecker and ordinary product are used. We introduce a ring R using the additive groups of the rational field and GF(s), and show that the Q(j,h,i) belong to a ring isomorphic to R. When s is a prime number, we show that R is the cyclotomic field. Finally, we show that the study of the X.j and X′.jX.j can be done in a much simpler manner, in terms of certain relatively small sized matrices over R.  相似文献   

19.
Supersaturated designs (SSDs) offer a potentially useful way to investigate many factors with only few experiments in the preliminary stages of experimentation. This paper explores how to construct E(fNOD)E(fNOD)-optimal mixed-level SSDs using k-cyclic generators. The necessary and sufficient conditions for the existence of mixed-level k-circulant SSDs with the equal occurrence property are provided. Properties of the mixed-level k  -circulant SSDs are investigated, in particular, the sufficient condition under which the generator vector produces an E(fNOD)E(fNOD)-optimal SSD is obtained. Moreover, many new E(fNOD)E(fNOD)-optimal mixed-level SSDs are constructed and listed. The method here generalizes the one proposed by Liu and Dean [2004. kk-circulant supersaturated designs. Technometrics 46, 32–43] for two-level SSDs and the one due to Georgiou and Koukouvinos [2006. Multi-level k-circulant supersaturated designs. Metrika 64, 209–220] for the multi-level case.  相似文献   

20.
For a fixed number of runs, not all 2nm designs with resolution III or IV have clear two-factor interactions. Therefore, it is highly desirable to know when resolution III or IV designs can have clear two-factor interactions. In this paper, we provide a unified geometrical study of this problem and give a complete classification of the existence of clear two-factor interactions in regular 2nm designs with resolution III or IV and reveal the structures of these designs.  相似文献   

设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号