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1.
Robustness of group divisible (GD) designs is investigated, when one block is lost, in terms of efficiency of the residual design. The exact evaluation of the efficiency can be made for singular GD and semi-regular GD designs as ell as regular GD designs with λ1 = 0. In a regular GD design with λ1 > 0, the efficiency may depend upon the lost block and sharp upper and lower bounds on the efficiency are presented. The investigation shows that GD designs are fairly robust in terms of efficiency. As a special case, we can also show the robustness of balanced incomplete block design when one block is lost. 相似文献
2.
J.S. Parihar 《Journal of statistical planning and inference》1980,4(3):321-323
The paper lists four new group divisible designs which are obtained by trial and error. These designs are believed to be new, since they are not listed in Clatworthy (1973), Freeman (1976) or John and Turner (1977). 相似文献
3.
The paper lists fourteen new group divisible PBIB/2 designs, which were obtained using the computer program described in John (1976). 相似文献
4.
In this paper a neat construction is provided for three new families of group divisible designs that generalize some designs from Clatworthy's table of the only 11 designs with two associate classes that have block size four, three groups, and replication numbers at most 10. In each case (namely, λ1=4 and λ2=5, λ1=4 and λ2=2, and λ1=8 and λ2=4), we have proved that the necessary conditions found are also sufficient for the existence of such GDD's with block size four and three groups, with one possible exception. 相似文献
5.
D.V.S. Sastry 《统计学通讯:理论与方法》2013,42(5-6):1677-1682
Bose and Shrikhande C19763 proved that if D(m, k, ?) is a Baer subdesign of another SBIBD D1 (v1, k1 ?), k1>k, then it also contains a complementary subdesign D* which is symmetric GDD, D* (v*, k*; ?-1, ?; m, n). Utilising this, we give a necessary condition for a SBIBD D to be a Baer subdesign of D1 and also give the parameters. Some GD designs are constructed. 相似文献
6.
K.A. Bush 《Journal of statistical planning and inference》1979,3(4):387-394
By a family of designs we mean a set of designs whose parameters can be represented as functions of an auxiliary variable t where the design will exist for infinitely many values of t. The best known family is probably the family of finite projective planes with υ = b = t2 + t + 1, r = k = t + 1, and λ = 1. In some instances, notably coding theory, the existence of families is essential to provide the degree of precision required which can well vary from one coding problem to another. A natural vehicle for developing binary codes is the class of Hadamard matrices. Bush (1977) introduced the idea of constructing semi-regular designs using Hadamard matrices whereas the present study is concerned mostly with construction of regular designs using Hadamard matrices. While codes constructed from these designs are not optimal in the usual sense, it is possible that they may still have substantial value since, with different values of λ1 and λ2, there are different error correcting capabilities. 相似文献
7.
Dieter Jungnickel 《Journal of statistical planning and inference》1979,3(3):273-278
Given any affine design with parameters v, b, r, k, λ and μ = k2/v and any design with parameters v′, b′, r′, k′, λ′ where r′ = tr for some natural number `t and k′?r, we construct a group divisible design with parameters v′' = vv′, m = v′, n = v, b′' = vb′, k′' = kk′, r′'= kr′, λ1 = tkλ and λ2 = μλ′. This is applied to some series of designs. As a lemma, we also show that any 0-1-matrix with row sums tr and column sums ?r may be written as the sum of r 0-1-matrices with row sums t and column sums ?1. 相似文献
8.
《Journal of statistical planning and inference》1996,52(2):241-253
We introduce new difference methods and apply them to construct group divisible designs with regular automorphism groups. 相似文献
9.
Generalizing methods of constructions of Hadamard group divisible designs due to Bush (1979), some new families of semi-regular or regular group divisible designs are produced. Furthermore, new nonisomorphic solutions for some known group divisible designs are given, together with useful group divisible designs not listed in Clatworthy (1973). 相似文献
10.
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
11.
R.C. Bose 《Journal of statistical planning and inference》1977,1(1):87-101
A symmetric group divisible design (SGDD) is said to have the dual property, if the dual of the design has the same parameters as the original design. In this paper we study the structure of such designs and give some applications to Baer subdesigns of symmetric balanced incomplete block designs (SBIBD) and to near planes (Fast-blockpläne). 相似文献
12.
In this paper a method of constructing group-divisible incomplete block designs has been suggested. A series of balanced incomplete block designs has also been obtained. 相似文献
13.
《Journal of statistical planning and inference》2004,119(2):401-410
In this paper, we present a general construction of group divisible designs and rectangular designs by utilising resolvable and “almost resolvable” balanced incomplete block designs. As special cases, we obtain the following E-optimal designs: (a) Group divisible (GD) designs with λ2=λ1+1 and (b) Rectangular designs with 2 rows and having λ3=λ2−1=λ1+1. Many of the GD designs are optimal among binary designs with regard to all type 1 criteria. 相似文献
14.
Basudeb Adhikary Rajendranath Panda 《Journal of statistical planning and inference》1983,7(4):387-405
In this paper some experimental situations are identified corresponding to which suitable response surface designs do not exist. A class of response surface designs is introduced to cope with these situations. Their analysis with and without blocking and methods of construction is discussed. 相似文献
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16.
A design is said to be super-simple if the intersection of any two blocks has at most two elements. In statistical planning of experiments, super-simple designs are the ones providing samples with maximum intersection as small as possible. Super-simple GDDs are useful in constructing super-simple BIBDs. The existence of super-simple (4,λ)‐GDDs has been determined for λ=2-6. In this paper, we investigate the existence of a super-simple (4,9)-GDD of group type gu and show that such a design exists if and only if u≥4, g(u−2)≥18 and u(u−1)g2≡0 (mod 4). 相似文献
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18.
The paper provides methods of construction of group divisible designs with block sizes three and four through balanced incomplete block and partially balanced incomplete block designs of block sizes 3 and 4. Furthermore, four non-isomorphic solutions are given. 相似文献
19.
K. A. Bush 《Journal of statistical planning and inference》1984,10(3):335-343
A class of designs with property C(t) are introduced for the first time, and their applications in group testing of samples are studied. 相似文献
20.
Sudhir Gupta 《统计学通讯:理论与方法》2013,42(11):3865-3868
A wide class of block designs for symmetrical parallel line assays with even number of doses, obtainable through group divisible designs is considered. Several new designs can thus be obtained using group divisibledesigns. Group divisible designs are also shown to provide a unification of many exisiting designs which follow as special cases. 相似文献