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Optimal chemical balance weighing designs for \(v+1\) objects. (English) Zbl 1248.62128
Summary: The paper studies the estimation problem of individual weights of objects using a chemical balance weighing design under the restriction on the number times in which each object is weighed. Conditions under which the existence of an optimum chemical balance weighing design for \(p = v\) objects implies the existence of an optimum chemical balance weighing design for \(p = v + 1\) objects are given. The existence of an optimum chemical balance weighing design for \(p = v + 1\) objects implies the existence of an optimum chemical balance weighing design for each \(p < v + 1\). A new construction method for optimum chemical balance weighing designs for \(p = v + 1\) objects is given. It uses the incidence matrices of ternary balanced block designs for \(v\) treatments.
MSC:
62K05 Optimal statistical designs
62K10 Statistical block designs
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References:
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