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Estimation of Unknown Object Measures in a Chemical Weighing Design with Correlated Errors
In this paper, some problems that concern the determining of unknown measurements of objects in the model of a chemical balance weighing design are presented. These designs are tested under the assumption that measurement errors are correlated and have the same variances. The relations between the parameters of a weighing design are considered from the point of view of the D-optimality criterion. We give some conditions determining the dependencies between the parameters of such designs and construction examples.
A study of the efficiency of chemical balance weighing designs
Abstract Some elements concerning the problem of determining chemical balance designs are considered. A method is presented for determining the best design in classes where no D-optimal design exists. In this case, we obtain a design that is highly D-efficient. The efficiency of such a design is presented as a function of the number of parameters and measurements, and its properties are studied. Charts showing the efficiency function for selected classes of designs are presented.
New classes of D-optimal chemical balance weighing designs with correlated errors
Summary This study presents several results concerning the determination of chemical balance weighing designs that satisfy the criterion of D-optimality. The designs are examined under the assumption that all measurements exhibit equal positive correlation and identical variances. We introduce a method for augmenting a regular D-optimal chemical balance weighing design with additional measurements in order to obtain a highly D-efficient chemical balance weighing design.
D-optimal chemical balance weighing designs with positively correlated errors: part I
Summary In this paper we consider issues related to the determination of chemical balance weighing designs satisfying the criterion of D-optimality. This problem is considered under the assumption that the measurements are equally positively correlated and they have the same variances. We answer the question of how to add four runs to a regular D-optimal chemical balance weighing design in order to obtain a highly D-efficient design. The problem formulated in this way leads to an extension of results contained in a previous paper in Biometrical Letters.
D-optimal chemical balance weighing designs with positively correlated errors: part II
Summary Some questions related to the problem of determining a chemical balance weighing design satisfying the criterion of D-optimality are considered. The theory is based on the assumption that the measurements are equally positively correlated and have the same variances. In this paper, we present a method of adding three measurements to a regular D-optimal chemical balance weighing designs to obtain a highly D-efficient chemical balance weighing design. The problem formulated in this way is an extension of results contained in a paper previously published in Biometrical Letters.
D-optimal chemical balance weighing designs with positively correlated errors: part III
Summary In this paper we consider issues related to the determination of chemical balance weighing designs satisfying the criterion of D-optimality. This problem is considered under the assumption that the measurements are equally positively correlated and they have the same variances. We answer the question of how to add four runs to a regular D-optimal chemical balance weighing design in order to obtain a highly D-efficient design. The problem formulated in this way leads to an extension of results contained in a previous paper in Biometrical Letters .
Contribution to spring balance weighing designs
Summary In this paper, we present some new results regarding spring balance weighing designs. We consider issues with regard to conditions for the existence of optimal designs, and give examples of optimal designs.
Notes on the Efficiency of Spring Balance Weighing Designs with Correlated Errors for An Even Number of Objects
In this paper, some issues regarding the efficiency of spring balance weighing designs for a selected class are presented. We give some conditions determining the relations between the parameters of such designs and construction examples.