Optimum chemical balance weighing designs under the restriction on weighings

Bronisław Ceranka; Małgorzata Graczyk

Discussiones Mathematicae Probability and Statistics (2001)

  • Volume: 21, Issue: 2, page 111-120
  • ISSN: 1509-9423

Abstract

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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 weighing design under the restriction on the number in which each object is weighed.

How to cite

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Bronisław Ceranka, and Małgorzata Graczyk. "Optimum chemical balance weighing designs under the restriction on weighings." Discussiones Mathematicae Probability and Statistics 21.2 (2001): 111-120. <http://eudml.org/doc/287663>.

@article{BronisławCeranka2001,
abstract = {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.},
author = {Bronisław Ceranka, Małgorzata Graczyk},
journal = {Discussiones Mathematicae Probability and Statistics},
keywords = {chemical balance weighing design; ternary balanced block design; ternary balanced block designs},
language = {eng},
number = {2},
pages = {111-120},
title = {Optimum chemical balance weighing designs under the restriction on weighings},
url = {http://eudml.org/doc/287663},
volume = {21},
year = {2001},
}

TY - JOUR
AU - Bronisław Ceranka
AU - Małgorzata Graczyk
TI - Optimum chemical balance weighing designs under the restriction on weighings
JO - Discussiones Mathematicae Probability and Statistics
PY - 2001
VL - 21
IS - 2
SP - 111
EP - 120
AB - 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.
LA - eng
KW - chemical balance weighing design; ternary balanced block design; ternary balanced block designs
UR - http://eudml.org/doc/287663
ER -

References

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  1. [1] K.S. Banerjee, Weighing Designs for Chemistry, Medicine, Economics, Operations Research, Statistics, Marcel Dekker Inc., New York 1975. Zbl0334.62030
  2. [2] E.J. Billington, Balanced n-array designs: a combinatorial survey and some new results, Ars Combinatoria 17 A (1984), 37-72. Zbl0537.05004
  3. [3] E.J. Billington and P.J. Robinson, A list of balanced ternary designs with r ≤ 15, and some necessary existence conditions, Ars Combinatoria 16 (1983), 235-258. Zbl0534.05010
  4. [4] B. Ceranka and K. Katulska, Chemical balance weighing designs under the restriction on the number of objects placed on the pans, Tatra Mt. Math. Publ., 17 (1999), 141-148. Zbl0988.62047
  5. [5] B. Ceranka, K. Katulska and D. Mizera, The application of ternary balanced block designs to chemical balance weighing designs, Discuss. Math. Algebra and Stochastic Methods 18 (1998), 179-185. Zbl0922.62074
  6. [6] H. Hotelling, Some improvements in weighing and other experimental techniques, Ann. Math. Stat., 15 (1944), 297-305. Zbl0063.02076
  7. [7] D. Raghavarao, Constructions and Combinatorial Problems in Designs of Experiments, John Wiley Inc., New York 1971. 
  8. [8] C.R. Rao, Linear Statistical Inference and its Applications, Second Edition, John Wiley Inc., New York 1973. Zbl0256.62002
  9. [9] M.N. Swamy, Use of balanced bipartite weighing designs as chemical balance designs, Comm. Statist. Theory Methods 11 (1982), 769-785. Zbl0514.62086

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