Displaying similar documents to “ X −1 -balance of some partially balanced experimental designs with particular emphasis on block and row-column designs ”

D-optimal cyclic two-dimensional block designs.

Jagdish N. Srivastava, A. M. Wijetunga (1983)

Trabajos de Estadística e Investigación Operativa

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In this paper we consider a class of incomplete block designs in which every block is two dimensional. Thus heterogeneity is removed not only between blocks, but also in two directions within each block. Such designs have been considered before in Srivastava (1977,1978). Here, we consider the class of cyclic designs of this type when the number of treatments ν is an odd number between 5 and 25, and present designs that are D-optimal within this class.

Optimal chemical balance weighing designs for v + 1 objects

Bronisław Ceranka, Małgorzata Graczyk (2003)

Kybernetika

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The paper studies the estimation problem of individual weights of objects using a chemical balance weighing design under the restriction on the number times in which each object is weighed. Conditions under which the existence of an optimum chemical balance weighing design for p = v objects implies the existence of an optimum chemical balance weighing design for p = v + 1 objects are given. The existence of an optimum chemical balance weighing design for p = v + 1 objects implies the existence of an optimum...

A note on the relations between two ternary balanced block designs and chemical balance weighing designs

Katarzyna Ambroży, Bronisław Ceranka (2001)

Discussiones Mathematicae Probability and Statistics

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The paper studied the problem of estimating of the weights of p objects in n weighings using a chemical balance weighing design under the restriction on the number of objects which can be placed on the right and left pans, respectively. Conditions under which the estimated weights are uncorrelated are given. The incidence matrices of two ternary balanced block designs which are used to construct chemical balance weighing designs satisfying these conditions are considered.

Optimum chemical balance weighing designs under the restriction on weighings

Bronisław Ceranka, Małgorzata Graczyk (2001)

Discussiones Mathematicae Probability and Statistics

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The paper deals with the problem of estimating individual weights of objects, using a chemical balance weighing design under the restriction on the number in which each object is weighed. A lower bound for the variance of each of the estimated weights from this chemical balance weighing design is obtained and a necessary and sufficient condition for this lower bound to be attained is given. The incidence matrix of ternary balanced block design is used to construct optimum chemical balance...

A unified terminology in block designs

Tadeusz Caliński, Sanpei Kageyama (2004)

Discussiones Mathematicae Probability and Statistics

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Partially efficiency balanced (PEB) designs with m efficiency classes have been defined by Puri and Nigam [15] as block designs which have simple analysis and, if properly used, allow the important contrasts to be estimated with desired efficiency. Such designs can be made available in varying replications and/or unequal block sizes. However, any block design is a PEB design with m efficiency classes for some m < v, where v is the number of treatments in the design. So the term "PEB"...

Evaluation of experimental designs in durum wheat trials

Anastasios Katsileros, Christos Koukouvinos (2015)

Biometrical Letters

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Variability among experimental plots may be a relevant problem in field genotype experiments, especially when a large number of entries are involved. Four field trials on 24 durum wheat genotypes were conducted in 2013/14 in order to evaluate the efficiency of Incomplete Block, Alpha and Augmented designs in comparison with the traditional Randomized Complete Block Design (RCBD). The results showed that the RCBD can be replaced by an Alpha design, which provides better control of variability...

On a characterization of symmetric balanced incomplete block designs

R.N. Mohan, Sanpei Kageyama, M.M. Nair (2004)

Discussiones Mathematicae Probability and Statistics

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All the symmetric balanced incomplete block (SBIB) designs have been characterized and a new generalized expression on parameters of SBIB designs has been obtained. The parameter b has been formulated in a different way which is denoted by bi, i = 1, 2, 3, associating with the types of the SBIB design Di. The parameters of all the designs obtained through this representation have been tabulated while corresponding them with the suitable formulae for the number ofblocks bi and the expression...

Some observations on the constructions of chemical balance weighing designs

Ratnakaram Nava Mohan, Bronisław Ceranka, Sanpei Kageyama (2001)

Discussiones Mathematicae Probability and Statistics

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The construction of some optimum chemical balance weighing designs from affine μ-resolvable balanced incomplete block (BIB) designs are discussed in the light of a characterization theorem on the parameters of affine μ-resolvable BIB designs as given by Mohan and Kageyama (1982), for the sake of practical use of researchers who need some selective designs for the construction of chemical balance weighing designs.

Incomplete split-block designs constructed by affine α-resolvable designs

Kazuhiro Ozawa, Shinji Kuriki, Stanisław Mejza (2017)

Biometrical Letters

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We construct an incomplete split-block design (ISBD) by the semi- Kronecker product of two affine α-resolvable designs for row and column treatments. We characterize such ISBDs with respect to the general balance property and we give the stratum efficiency factors for the ISBDs.

Some applications of weighing designs

Małgorzata Graczyk (2013)

Biometrical Letters

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The purpose of this paper is to apply results on weighing designs to the setting of 2m factorial designs. Using weighing designs, we give some proposals for experimental plans. Relevant counterexamples are indicated. Also the results of a simulation study on the existence of weighing designs are presented.