Completely balanced block designs with nonuniform block dimension
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Relations between regular A-optimal chemical and spring balance weighing designs with diagonal covariance matrix of errors
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.
Connectedness of row and column designs
Some D-optimal chemical balance weighing designs: theory and examples
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.
Optimum chemical balance weighing designs under the restriction on weighings
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 weighing...
Optimum chemical balance weighing designs with diagonal variance-covariance matrix of errors
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 bound is attained...
A note on the relations between two ternary balanced block designs and chemical balance weighing designs
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.
Optimal chemical balance weighing designs for objects
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 objects implies the existence of an optimum chemical balance weighing design for objects are given. The existence of an optimum chemical balance weighing design for objects implies the existence of an optimum chemical...
Robustness optimal spring balance weighing designs for estimation total weight
In this paper we develop the theory of spring balance weighing designs with non-positive correlated errors for that the lower bound of the variance of estimated total weight is attained.
Orthogonality, efficiency and balance of a block design
The authors discuss the interconnections between the concepts of orthogonality, efficiency, and balance of block designs. No new theorems are obtained. Illustrative examples are presented. MR0707816
Some observations on the constructions of chemical balance weighing designs
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.
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