Chemical Balance Weighing Design with Different Variances of Errors
- Cite this paper as:
- Ceranka B., Graczyk M. (2005) Chemical Balance Weighing Design with Different Variances of Errors. In: Baier D., Wernecke KD. (eds) Innovations in Classification, Data Science, and Information Systems. Studies in Classification, Data Analysis, and Knowledge Organization. Springer, Berlin, Heidelberg
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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