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Robustness of Optimal Chemical Balance Weighing Designs for Estimation of Total Weight
Communications in Statistics - Theory and Methods, 2012The subject of our study is the chemical balance weighing design in which the errors are correlated and have equal variances. A lower bound for the variance of estimated total weight is obtained and the necessary and sufficient conditions for the attainability of this lower bound are given.
Bronisław Ceranka, Małgorzata Graczyk
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A-optimal Chemical Balance Weighing Designs with Diagonal Covariance Matrix of Errors
2001The paper deals with the problem of estimating the weights of objects using an A-optimal chemical balance weighing design with the covariance matrix of errors o2G, where G is an n x n known positive definite diagonal matrix. A lower bound of tr(X’G-1X)-1is obtained and a necessary and sufficient condition for this lower bound to be attained is given ...
B. Ceranka, K. Katulska
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New Construction of Optimum Chemical Balance Weighing Designs
Calcutta Statistical Association Bulletin, 1987The present paper deals with certain chemical balance weighing designs. The incidence matrices of BIB designs for v treatments have been used to construct these designs for p = v + 1 objects. Conditions have been obtained for making some of these designs “optimum”.
Ceranka, B., Katulska, K.
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On certain A-optimal chemical balance weighing designs
Computational Statistics & Data Analysis, 2007zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ceranka, B., Graczyk, M., Katulska, K.
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On Some Chemical Balance Weighing Designs
Australian Journal of Statistics, 1971SummaryThe present paper deals with certain chemical balance weighing designs. The incidence matrices of BIB designs and balanced ternary designs have been used to construct these designs. Conditions have been obtained to make some of these designs “optimum”.
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New classes of D-optimal chemical balance weighing designs with correlated errors
Biometrical LettersSummary This study presents several results concerning the determination of chemical balance weighing designs that satisfy the criterion of D-optimality.
M. Graczyk, B. Ceranka, Teresa Oliveira
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On adaptive chemical balance weighing designs
Journal of Statistical Planning and Inference, 1987We consider the problem of weighing n objects in N weighings \((N>n\), \(N\equiv 1 mod 4)\) on a chemical balance. In case all but one weighing has been realized we treat an adaptive choice for allocating the n objects in the last weighing. This design is shown to be better than the A-optimal deterministic design with respect to some suitably modified ...
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A relation between BIB designs and chemical balance weighing designs
Statistics & Probability Letters, 1987The paper gives a certain new construction method for optimum chemical balance weighing designs. It utilizes a relation between the incidence matrices of a set of BIB designs and the design matrix of a chemical balance weighing design.
Ceranka, B., Katulska, K.
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Communications in Statistics - Theory and Methods, 1992
This paper provides D-optimal spring balance designs for estimating individual weights when the number of objects to be weighed in each weighing, B, is fixed. D-optimal chemical balance designs for estimating total weight under both homogeneous and nonhomogeneous error variances are found when the number of objects weighed in each weighing is ≥ B, a ...
Feifei Wei, William I. Notz
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This paper provides D-optimal spring balance designs for estimating individual weights when the number of objects to be weighed in each weighing, B, is fixed. D-optimal chemical balance designs for estimating total weight under both homogeneous and nonhomogeneous error variances are found when the number of objects weighed in each weighing is ≥ B, a ...
Feifei Wei, William I. Notz
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Note on the construction of optimum chemical balance weighing designs
Annals of the Institute of Statistical Mathematics, 1983Sufficient conditions for the existence of certain optimum chemical balance weighing designs are investigated.
Kageyama, S., Saha, G. M.
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