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1.
ABSTRACT

Neighbor designs are recommended for the cases where the performance of treatment is affected by the neighboring treatments as in biometrics and agriculture. In this paper we have constructed two new series of non binary partially neighbor balanced designs for v = 2n and v = 2n+1 number of treatments, respectively. The blocks in the design are non binary and circular but no treatment is ever a neighbor to itself. The designs proposed here are partially balanced in terms of nearest neighbors. No such series are known in the literature.  相似文献   

2.
A generalized neighbor design relaxes the equality condition on the number of times two treatments as neighbors in the design. In this article, we have considered the construction of some classes of generalized neighbor designs with block size k=3 by using the method of cyclic shifts. The distinguishing feature of this construction method is that the properties of a design can easily be obtained from the sets of shifts instead of constructing the actual blocks of the design. A catalog of generalized neighbor designs with block size k=3 is compiled for v∈{5,6,…,18} treatments and for different replications. We provide the reader with a simpler method of construction, and in general the catalog that gives an open choice to the experimenter for selecting any class of neighbor designs.  相似文献   

3.
In this article, a general method of construction of neighbor block designs is given. The designs are constructed using variation of a simple method which we refer to as the method of addition (renamed as the method of cyclic shifts). We give complete solution of neighbor balanced designs for k = 4 for any value of v. We also give many series of generalized neighbor designs (GNDs). In the last section, we have constructed GNDs in a sequential manner (as Did John 1981) for v ≤ 50 and r is multiple of k.  相似文献   

4.
The problem considered is that of finding D-optimal design for the estimation of covariate parameters and the treatment and block contrasts in a block design set up in the presence of non stochastic controllable covariates, when N = 2(mod 4), N being the total number of observations. It is clear that when N ≠ 0 (mod 4), it is not possible to find designs attaining minimum variance for the estimated covariate parameters. Conditions for D-optimum designs for the estimation of covariate parameters were established when each of the covariates belongs to the interval [?1, 1]. Some constructions of D-optimal design have been provided for symmetric balanced incomplete block design (SBIBD) with parameters b = v, r = k = v ? 1, λ =v ? 2 when k = 2 (mod 4) and b is an odd integer.  相似文献   

5.
Neighbor balance designs were first introduced by Rees (1967) in circular blocks for the use in serological research. Subsequently several researchers have defined the neighbor designs in different ways. In this paper, neighbor balance circular designs for (kv) block size are constructed for even number of treatments i.e. v=2n. No such series of designs is known in literature. Two theorems are developed for circular designs. Theorem 1 gives the non-binary circular blocks, whereas Theorem 2 generates binary circular blocks when n≤4 and non-binary blocks for n>4. In suggested designs no treatment is ever a neighbor of itself. Blocks are constructed in such a way that each treatment is a right and left neighbor of every other treatment for a fixed number of times say λ. Sizes of initial circular blocks are not same. One main guiding principle for such designs is to ensure economy in material use.  相似文献   

6.
In this paper, some infinite series of generalized neighbor designs are constructed for the linear blocks which are useful to balance out the neighbor effects for the cases where (a) one of the v treatments has some neighbor effects with other treatments, while remaining (v – 1) treatments have half of that neighbor effect among selves, (b) some of the v treatments have some neighbor effect with other treatments, while remaining treatments have half of that neighbor effect among themselves, (c) one of the v treatments has some neighbor effect with other treatments, while remaining (v – 1) treatments have double of that effect among themselves, and (d) some of the v treatments have some neighbor effect with other, while remaining treatments have double of it among themselves.  相似文献   

7.
Neighbor designs have their own importance in the experiments to remove the neighbor effects where the performance of a treatment is affected by the treatments applied to its adjacent plots. If each pair of distinct treatments appears exactly once as neighbors, neighbor designs are called minimal. Most of the neighbor designs require a large number of blocks of equal sizes. In this situation minimal neighbor designs in unequal block sizes are preferred to reduce the experimental material. In this article some series are presented to construct minimal neighbor designs in circular blocks of unequal sizes.  相似文献   

8.
Neighbor designs are useful to neutralize the neighbor effects. In literature, most of the constructed neighbor designs are in circular blocks but linear blocks have more practical application in field experiments. In this article, some infinite series of minimal neighbor designs are constructed in proper linear blocks. There are many situations where minimal neighbor designs cannot be constructed in proper linear blocks. To overcome this problem neighbor designs in improper linear blocks and GN2-designs in proper linear blocks are constructed.  相似文献   

9.
Some new neighbor designs are presented here. Second-order neighbor designs for different configurations are generated in circular binary blocks. Third-order and fourth-order neighbor designs for some cases are also constructed. In all cases, circular blocks are well separated and these designs are obtained through initial block/s. At the end of the study, some models for analysis of these designs are also presented.  相似文献   

10.
ABSTRACT

This paper describes some methods of constructing circular neighbor balanced and circular partially neighbor balanced block designs for estimation of direct and neighbor effects of the treatments. A class of circular neighbor balanced block designs with unequal block sizes is also proposed.  相似文献   

11.
A new exchange algorithm for the construction of (M, S)-optimal incomplete block designs (IBDS) is developed. This exchange algorithm is used to construct 973 (M, S)-optimal IBDs (v, k, b) for v= 4,…,12 (varieties) with arbitrary v, k (block size) and b (number of blocks). The efficiencies of the “best” (M, S)-optimal IBDs constructed by this algorithm are compared with the efficiencies of the corresponding nearly balanced incomplete block designs (NBIBDs) of Cheng(1979), Cheng & Wu (1981) and Mitchell & John(1976).  相似文献   

12.
Neighbor-balanced designs are useful to remove the neighbor effects in experiments where the performance of a treatment is affected by the treatments applied to its adjacent neighbors. In this article, neighbor-balanced designs are constructed in linear blocks of (i) equal sizes and (ii) two different sizes k 1 and k 2.  相似文献   

13.
Polygonal designs are useful in survey sampling in terms of balanced sampling plans excluding contiguous units (BSECs) and balanced sampling plans excluding adjacent units (BSAs). In this article, the method of cyclic shifts has been used for the construction of cyclic polygonal designs (in terms of BSAs) with block size k = 3 and λ = 1, 2, 3, 4, 6, 12 for joint distance α = 2 and 51 new designs for treatments v ≤ 100 are given.  相似文献   

14.
ABSTRACT

The study of r-out-of-n systems is of utmost importance in reliability theory. In this note, we study closure of different partial orders under the formation of r-out-of-N and (N ? s)-out-of-N systems when the number of components N, forming the system, is a random variable having support {k, k + 1,…}, where k is a fixed positive integer, r ∈ {1,…, k} and s ∈ {0, 1,…, k ? 1}. This generalizes quite a few results already known in the literature. We also study the closure of different partial orders when two systems are formed out of different random number of components.  相似文献   

15.
A generalized neighbor design relaxes the equality condition on the number of times two treatments occur as neighbors in the design. In this article we have constructed a new series of generalized neighbor designs with equal block sizes, a series of neighbor designs of Rees [1967. Some designs of use in serology. Biometrics 23, 779–791] and a series of neighbor designs with two distinct block sizes. Two more new series of GN2 designs are also constructed for even number of treatments. It has been shown that quasi neighbor designs introduced by Preece [1994. Balanced Ouchterlony neighbor designs. J. Combin. Math. Combin. Comput. 15, 197–219] are special cases of generalized neighbor designs with t=2t=2. All the designs given here are binary. A new definition—partially balanced circuit design is introduced which is a special case of generalized neighbor designs with binary blocks.  相似文献   

16.
This article deals with residual treatment effects designs for the purpose of comparing v test treatments with a control treatment when the number of periods is no larger than v + 1. Control balanced residual treatment effects designs, which are Schur-optimal, are considered. Some methods of their construction are given.  相似文献   

17.
Neighbor designs are useful to neutralize the neighbor effects. In this paper two classes of these designs are constructed in circular binary blocks of size 4, 8, …, 24. First class consists of six infinite series of nearest neighbor designs in which each pair of distinct treatments appears once as neighbors. Second class also deals with six infinite series of these designs in which each pair of distinct treatments appears twice as neighbors. A catalog of nearest neighbor designs is also compiled in circular binary blocks for odd number of treatments from 23 to 99.  相似文献   

18.
In this article, the exchange and interchange algorithm of Zergaw (1989 Zergaw , G. ( 1989 ). A sequential method of constructing optimal block designs . Austral. J. Statist. 31 : 333342 .[Crossref] [Google Scholar]) and Martin and Eccleston (1992 Martin , R. J. , Eccleston , J. A. ( 1992 ). Recursive formulae for constructing block designs with dependent errors . Biometrika 79 : 426430 .[Crossref], [Web of Science ®] [Google Scholar]) have been modified and used for searching efficient block designs for making all possible pairwise treatment comparisons when observations are dependent. The lower bounds to the A- and D-efficiencies of the designs in a given class of the designs have been obtained for correlated observation structure and the procedure of computing lower bounds to A- and D-efficiencies has been incorporated in the algorithm. The algorithm has been translated into a computer program using Microsoft Visual C++. Using this program, a search for efficient designs for making all possible pairwise treatment comparisons has been made for v ≤ 10, b ≤ 33, k ≤ 10 such that bk ≤ 100 and v > k. The block designs considered are usual block designs (rectangular block designs) and circular block designs. Nearest neighbor (NN), autoregressive of order 1 (AR(1)) correlation structures are studied. The ranges of correlation coefficients for different correlation structures investigated are |ρ|≤0.50 for NN correlation structure in rectangular blocks, |ρ|≤0.45 for NN correlation structure in circular blocks, and |ρ|≤0.95 for AR(1) correlation structure. For these ranges, the matrix of correlation coefficients among observations within a block is positive definite. Robustness aspects of designs that are efficient for a given value of correlation have been investigated against other values of correlation coefficients. Robustness aspects of designs that are efficient for independent observations have also been studied for experimental situations with dependent observations.  相似文献   

19.
Neighbor balanced designs are used to remove the neighbor effects but most of these designs require a large number of blocks. To neutralize the neighbor effects in such situations, GN2-designs are most desirable. This article deals with the (i) refinement of some series of GN2-designs constructed by Zafaryab et al. (2010) and (ii) construction of some new series of GN2-designs in circular blocks of equal size.  相似文献   

20.
Generalized neighbor designs relax the condition of constancy on the number of times two treatments occur as neighbors in a design. In this paper, we constructed generalized neighbor designs in circular blocks of equal size. Catalogs of these designs for block size 5, 7 and 9 are also compiled. All the designs given here are binary.  相似文献   

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