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

100%
Ceranka B., Graczyk M.
Biometrical Letters
|
2017
|
tom 54
|
nr 2
137-154
EN
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.
2
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A note on the relations between two ternary balanced block designs and chemical balance weighing designs

100%
Ambroży K., Ceranka B.
Discussiones Mathematicae Probability and Statistics
|
2001
|
tom 21
|
nr 1
5-10
EN
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.
3
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Optimum chemical balance weighing designs under the restriction on weighings

100%
Ceranka B., Graczyk M.
Discussiones Mathematicae Probability and Statistics
|
2001
|
tom 21
|
nr 2
111-120
EN
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 design under the restriction on the number in which each object is weighed.
4
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Relations between regular A-optimal chemical and spring balance weighing designs with diagonal covariance matrix of errors

80%
Ceranka B., Graczyk M.
Biometrical Letters
|
2013
|
tom 50
|
nr 2
127-136
EN
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.
5
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Some applications of weighing designs

80%
Graczyk M.
Biometrical Letters
|
2013
|
tom 50
|
nr 1
15-26
EN
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.
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