Displaying similar documents to “Some applications of weighing designs”

Relations between regular A-optimal chemical and spring balance weighing designs with diagonal covariance matrix of errors

Bronisław Ceranka, Małgorzata Graczyk (2013)

Biometrical Letters

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In this paper, we study the relationships between regular A-optimal spring balance weighing designs and regular A-optimal chemical balance weighing designs. We give the basic relation between these designs in the case where the errors are uncorrelated and they have different variances. We give some examples of methods of construction of such designs.

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J. López-Fidalgo (2009)

Boletín de Estadística e Investigación Operativa. BEIO

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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...

Some D-optimal chemical balance weighing designs: theory and examples

Bronisław Ceranka, Małgorzata Graczyk (2017)

Biometrical Letters

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In this paper we study a certain kind of experimental designs called chemical balance weighing designs. We consider issues with regard to determining optimality conditions. We give new classes of designs in which we are able to determine an optimal design. Moreover, examples are given for the presented cases.

D-optimal and highly D-efficient designs with non-negatively correlated observations

Krystyna Katulska, Łukasz Smaga (2016)

Kybernetika

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In this paper we consider D-optimal and highly D-efficient chemical balance weighing designs. The errors are assumed to be equally non-negatively correlated and to have equal variances. Some necessary and sufficient conditions under which a design is D*-optimal design (regular D-optimal design) are proved. It is also shown that in many cases D*-optimal design does not exist. In many of those cases the designs constructed by Masaro and Wong (2008) and some new designs are shown to be...

Adaptive biased-coin designs for clinical trials with several treatments

Anthony C. Atkinson (2004)

Discussiones Mathematicae Probability and Statistics

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Adaptive designs are used in phase III clinical trials for skewing the allocation pattern towards the better treatments. We use optimum design theory to provide a skewed biased-coin procedure for sequential designs with continuous responses. The skewed designs are used to provide adaptive designs, the performance of which is studied numerically for designs with three treatments. Important properties are loss and the proportion of allocation to inferior treatments. Regularisation to provide...

Optimum chemical balance weighing designs with diagonal variance-covariance matrix of errors

Bronisław Ceranka, Małgorzata Graczyk (2004)

Discussiones Mathematicae Probability and Statistics

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In this paper we study the estimation problem of individual measurements (weights) of objects in a model of chemical balance weighing design with diagonal variance - covariance matrix of errors under the restriction k₁ + k₂ < p, where k₁ and k₂ represent the number of objects placed on the right and left pans, respectively. We want all variances of estimated measurments to be equal and attaining their lower bound. We give a necessary and sufficient condition under which this lower...

X −1 -balance of some partially balanced experimental designs with particular emphasis on block and row-column designs

Ryszard Walkowiak (2015)

Biometrical Letters

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This paper considers block designs and row-column designs where the information matrix C has two different nonzero eigenvalues, one of multiplicity 1 and the other of multiplicity h−1, where h is the rank of the matrix C. It was found that for each such design there exists a diagonal positive definite matrix X such that the design is X −1-balanced.

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...

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...

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.

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.

Control treatments in designs with split units generated by Latin squares

Shinji Kuriki, Iwona Mejza, Kazuhiro Ozawa, Stanisław Mejza (2014)

Biometrical Letters

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This paper deals with two-factor experiments with split units. The whole plot treatments occur in a repeated Latin square, modified Latin square or Youden square, while subplot treatments occur in a block design within the whole plots. The statistical properties of the considered designs are examined. Special attention is paid to the case where one of the treatments is an individual control or an individual standard treatment. In addition, we give a brief overview of work on the design...