共查询到20条相似文献,搜索用时 15 毫秒
1.
Masahide Kuwada 《Journal of statistical planning and inference》1982,7(1):39-48
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.
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
3.
Teruhiro Shirakura 《Journal of statistical planning and inference》1979,3(4):337-345
The norm 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
4.
Max D. Morris 《Journal of statistical planning and inference》1984,10(1):115-117
A lower bound is given for the number of experimental runs required in search designs for two-level factorial models. 相似文献
5.
Jennifer Seberry 《Journal of statistical planning and inference》1985,11(3):373-379
We show that the necessary conditions , , , are sufficient for the existence of a generalized Bhaskar Rao design GBRD(υ,b,r,3,λ;G) for the elementary abelian group G, of each order |G|. 相似文献
6.
Masahide Kuwada 《Journal of statistical planning and inference》1979,3(4):347-360
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.
Jeremy E. Dawson 《Journal of statistical planning and inference》1985,11(1):103-110
We give a construction for a generalized Hadamard matrix GH(4q, EA(q)) as a 4 × 4 matrix of q × q blocks, for q an odd prime power other than 3 or 5. Each block is a GH(q, EA(q)) and certain combinations of 4 blocks form GH(2q, EA(q)) matrices. Hence a GH(4q, EA(q)) matrix exists for every prime power q. 相似文献
8.
M.L. Aggarwal Mithilesh Kumar Jha Seema Gupta Sarah Garland 《Journal of statistical planning and inference》2010
5 and 6 have recently introduced power-sequence terraces. In this paper we have used these terraces for the construction of some new families of balanced cross-over designs of first and second order which are variance-balanced. We have also used them for the construction of some new families of balanced ternary cross-over designs. 相似文献
9.
Abdalla T. El-Helbawy 《Journal of statistical planning and inference》1984,10(1):105-113
A general approach for comparing designs of paired comparison experiments on the basis of the asymptotic relative efficiencies, in the Bahadur sense, of their respective likelihood ratio tests is discussed and extended to factorials. Explicit results for comparing five designs of 2q factorial paired comparison experiments are obtained. These results indicate that some of the designs which require comparison of fewer distinct pairs of treatments than does the completely balanced design are, generally, more efficient for detecting main effects and/or certain interactions. The developments of this paper generalize the work of Littell and Boyett (1977) for comparing two designs of R x C factorial paired comparison experiments. 相似文献
10.
Two matrices with elements taken from the set {-1,1} are Hadamard equivalent if one can be converted into the other by a sequence of permutations of rows and columns, and negations of rows and columns. In this paper we summarize what is known about the number of equivalence classes of matrices having maximal determinant. We establish that there are 7 equivalence classes for matrices of order 21 and that there are at least 9884 equivalence classes for matrices of order 26. The latter result is obtained primarily using a switching technique for producing new designs from old. 相似文献
11.
Bounds on the latest root of the C-matrix and the number of blocks for a variance-balanced block design are given. These results contain the well-known results as special cases. 相似文献
12.
Families of Repeated Measurements Designs balanced for residual effects are constructed (whenever the divisibility conditions allow), under the assumption that the number of periods is less than the number of treatments and that each treatment precedes each other treatment once. These designs are then shown to be connected for both residual and direct treatment effects. 相似文献
13.
This is a continuation of Part I of our previous paper (1980) on conbinatorial aspects of t-designs with t ≥ 2. Along the same developments as in Part I, this paper provides tables, assorted examples of t-designs, and interesting unsolved problems. A brief background and a short review of the literature related to each unsolved problem is also provided. Some tables list parameters of designs whose existence or nonexistence is not established in literature. Notation and numbering of Part I are still used here. 相似文献
14.
The set of distinct blocks of a block design is known as its support. We construct complete designs with parameters v(?7), k=3, λ=v ? 2 which contain a block of maximal multiplicity and with support size . Any complete design which contains such a block, and has parameters v, k, λ as above, must be supported on at most (v3) ? 4(v ? 2) blocks. Attention is given to complete designs because of their direct relationship to simple random sampling. 相似文献
15.
J.A. John 《Journal of statistical planning and inference》1981,5(1):99-105
Cotter, John and Smith (1973) have given conditions for an incomplete block design to have orthogonal factorial structure. Further results on the intra-block analysis of such designs are given. The concept of balance in factorial design is discussed and results are given which enable the degree of balance in generalised cyclic designs to be determined. 相似文献
16.
Jennifer Seberry 《Journal of statistical planning and inference》1984,10(1):69-82
Some recursive constructions are given for Bhaskar Rao designs. Using examples of these designs found by Shyam J. Singh, Rakesh Vyas and new ones given here we show the necessary conditions λ≡0 (mod 2), λυ(υ?1)≡0 (mod 24) are sufficient for the existence of Bhaskar Rao designs with one association class and block size 3. This result is used with a result of Street and Rodger to obtain regular partially balanced block designs with 2υ treatments, block size 3, λ1=0, group size 2 and υ groups. 相似文献
17.
A. Hedayat 《Journal of statistical planning and inference》1984,9(1):143-145
It is shown that within the class of connected binary designs with arbitrary block sizes and arbitrary replications only a symmetic balanced incomplete block design produces a completely symmetric information matrix for the treatment effects whenever the number of blocks is equal to the number of treatments and the number of experimental units is an integer multiple of the number of treatments. Such a design is known to be universally optimal. 相似文献
18.
Mike Jacroux 《Journal of statistical planning and inference》1985,11(3):385-398
In this paper, we investigate the problem of determining block designs which are optimal under type 1 optimality criteria within various classes of designs having υ treatments arranged in b blocks of size k. The solutions to two optimization problems are given which are related to a general result obtained by Cheng (1978) and which are useful in this investigation. As one application of the solutions obtained, the definition of a regular graph design given in Mitchell and John (1977) is extended to that of a semi-regular graph design and some sufficient conditions are derived for the existence of a semi-regular graph design which is optimal under a given type 1 criterion. A result is also given which shows how the sufficient conditions derived can be used to establish the optimality under a specific type 1 criterion of some particular types of semi- regular graph designs having both equal and unequal numbers of replicates. Finally,some sufficient conditions are obtained for the dual of an A- or D-optimal design to be A- or D-optimal within an appropriate class of dual designs. 相似文献
19.
J.Q. Longyear 《Journal of statistical planning and inference》1981,5(2):181-187
A nest with parameters (r,k,λ)→(r′,k′,λ′) is a BIBD on (b,v,r,k,λ) where each block has a distinguished sublock of cardinality k, the sublocks forming a (b,v,r,k,λ)-design.These designs are ‘nested’ in the sense of W.T. Federer (1972), who recommended the use of these designs for the sequential addition of periods in marketing experiments in order to retain Youden design properties as rows are added. Note that for a Youden design, the b columns and v treatments are in an SBIBD arrangement with parameters v=b, k=r, and λ. 相似文献
20.
This paper deals with the existence and nonexistence of BIB designs with repeated blocks. The approach is an algebraic one. The concept of a support matrix is introduced and some of its basic properties are noted. Some basic examples of support matrices are given when the block size is 3. The connection between full column rank proper support matrices and irreducible designs is explored and some examples of such matrices are given. 相似文献