A note on the relations between two ternary balanced block designs and chemical balance weighing designs

Katarzyna Ambroży; Bronisław Ceranka

Discussiones Mathematicae Probability and Statistics (2001)

  • Volume: 21, Issue: 1, page 5-10
  • ISSN: 1509-9423

Abstract

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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.

How to cite

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Katarzyna Ambroży, and Bronisław Ceranka. "A note on the relations between two ternary balanced block designs and chemical balance weighing designs." Discussiones Mathematicae Probability and Statistics 21.1 (2001): 5-10. <http://eudml.org/doc/287657>.

@article{KatarzynaAmbroży2001,
abstract = {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.},
author = {Katarzyna Ambroży, Bronisław Ceranka},
journal = {Discussiones Mathematicae Probability and Statistics},
keywords = {chemical balance weighing design; ternary balanced block desig; ternary balanced block design; chemical balance weighing designs},
language = {eng},
number = {1},
pages = {5-10},
title = {A note on the relations between two ternary balanced block designs and chemical balance weighing designs},
url = {http://eudml.org/doc/287657},
volume = {21},
year = {2001},
}

TY - JOUR
AU - Katarzyna Ambroży
AU - Bronisław Ceranka
TI - A note on the relations between two ternary balanced block designs and chemical balance weighing designs
JO - Discussiones Mathematicae Probability and Statistics
PY - 2001
VL - 21
IS - 1
SP - 5
EP - 10
AB - 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.
LA - eng
KW - chemical balance weighing design; ternary balanced block desig; ternary balanced block design; chemical balance weighing designs
UR - http://eudml.org/doc/287657
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] B. Ceranka and K. Katulska, On construction of optimum chemical balance weighing designs, J. Indian Statist. Ass. 26 (1988a), 27-30. Zbl0651.62072
  3. [3] B. Ceranka and K. Katulska, On some optimum chemical balance weighing designs for v + 1 objects, J. Japan Statist. Soc. 18 (1988b), 47-50. Zbl0651.62072
  4. [4] B. Ceranka and K. Katulska, Chemical balance weighing designs under the restriction on the number of objects placed on the pans, Tatra Mountains Mathematical Publications 17 (1999), 141-148. Zbl0988.62047
  5. [5] B. Ceranka, K. Katulska and D. Mizera, The application of ternary balanced block design to chemical balanced weighing designs, Discuss. Math. - Algebra and Stochastic Methods 18 (1998), 179-185. Zbl0922.62074
  6. [6] A. Dey, On some chemical balance weighing designs, Austral. J. Statist. 13 (1971), 137-141. Zbl0249.62080
  7. [7] S. Kageyama and G.M. Saha, Note on the construction of optimum chemical balance weighing designs, Ann. Inst. Statist. Math. 35 A (1983), 447-452. Zbl0553.62066
  8. [8] D. Raghavararao, Constructions and Combinatorial Problems in Designs of Experiments, John Wiley Inc., New York 1971. 
  9. [9] G.M. Saha, A note on relations between incomplete block and weighingdesigns, Ann. Inst. Statist. Math. 27 (1975), 387-390. Zbl0351.05015
  10. [10] G.M. Saha and S. Kageyama, Balanced arrays and weighing designs, Austral. J. Statist. 26 (1984), 119-124. Zbl0599.62089
  11. [11] M.N. Swamy, Use of balanced bipartite weighing designs as chemical balance designs, Commun. Statist. - Theor. Meth. 11 (1982), 769-785. Zbl0514.62086

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