Vol: 32 Page: 93

Authors:
Bronisław Ceranka
Małgorzata Graczyk

Title:
 Optimum chemical balance weighing designs based on balanced bipartite block designs and ternary balanced block designs

Language: English

Keywords:
balanced bipartite block design
chemical balance weighing design
ternary balanced block design

Summary:
In this paper we study the problem of estimating individual weights of objects in chemical balance weighing design. We assume that in each weighing operation not all objects are included. All variances of estimated weights are equal and they attain the lower bound. We give necessary and sufficient condition under which this lover bound is attain by variances of each of the estimated weights from this chemical balance weighing design. To construction of the design matrix X of optimal chemical balance weighing design we use the incidence matrices of balanced bipartite block designs and ternary balanced block designs.