Chemical Balance Weighing Design with Different Variances of Errors

  • Bronisław Ceranka
  • Małgorzata Graczyk
Conference paper
Part of the Studies in Classification, Data Analysis, and Knowledge Organization book series (STUDIES CLASS)

Abstract

The paper is studying the estimation problem of individual weights of objects using a chemical balance weighing design under the restriction on the number of times in which each object is weighed. We assume that errors are uncorrelated with different variances. The necessary and sufficient condition under which the lower bound of variance of each of the estimated weights is attained is given. For a new construction method of the optimum chemical balance weighing design we use the incidence matrices of the balanced incomplete block designs and the ternary balanced block designs.

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References

  1. BANERJEE, K.S. (1975): Weighing Designs for Chemistry, Medicine, Economics, Operations Research, Statistics. Marcel Dekker Inc., New York.Google Scholar
  2. BILLINGTON, E.J. and ROBINSON, P.J. (1983): A list of balanced ternary block designs with r ≤ 15 and some necessary existence conditions. Ars Combinatoria, 16, 235–258.MathSciNetGoogle Scholar
  3. CERANKA, B. and GRACZYK, M. (2001): Optimum chemical balance weighing designs under the restriction on weighings. Discussiones Mathematicae-Probability and Statistics 21, 111–121.MathSciNetGoogle Scholar
  4. CERANKA, B. and GRACZYK, M. (2003): Optimum chemical balance weighing designs. Tatra Mountains Math. Publ, 29, 1–9.MathSciNetGoogle Scholar
  5. HOTELLING, H. (1944): Some improvements in weighing and other experimental techniques. Ann. Math. Stat., 15, 297–305.MATHMathSciNetGoogle Scholar
  6. KATULSKA, K. (1989): Optimum chemical balance weighing designs with non-homogeneity of the variances of errors. J. Japan Statist. Soc, 19, 95–101.MATHMathSciNetGoogle Scholar
  7. RAGHAVARAO, D. (1971): Constructions and Combinatorial Problems in Designs of Experiments. John Wiley Inc., New York.Google Scholar

Copyright information

© Springer-Verlag Berlin · Heidelberg 2005

Authors and Affiliations

  • Bronisław Ceranka
    • 1
  • Małgorzata Graczyk
    • 1
  1. 1.Department of Mathematical and Statistical MethodsAgricultural University of PoznańPoznańPoland

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