A-optimal biased spring balance weighing design

summary:In this paper we study the problem of estimation of individual measurements of objects in a biased spring balance weighing design under assumption that the errors are uncorrelated and they have different variances. The lower bound for the variance of each of the estimated measurements for this design and the necessary and sufficient conditions for this lower bound to be attained are given. The incidence matrices of the balanced incomplete block designs are used for construction of the A-optimal biased spring balance weighing design

Optimum Chemical Balance Weighing Design under Certain Condition

2000 Mathematics Subject Classification: 62K05, 05B05.The problem of estimation of unknown weights of p objects is considered. The experiment is carried out according to the standard Gauss-Markoff model of the chemical balance weighing design. Existence conditions of the optimum design are given. New construction method of the optimum design based on the set of the incidence matrices of the ternary balanced block designs is presented

ON D-OPTIMAL CHEMICAL BALANCE WEIGHING DESIGNS

The paper deals with the problem of determining the chemical balance weighing designs satisfying the criterion of D-optimality under assumption that the measurement errors are equal correlated and they have the same variances. The existence conditions and the form of the optimal design are given. Moreover, some construction methods of the design matrices based on the incidence matrices of the balanced incomplete block designs and ternary balanced block designs are presented. Any example of construction is given

CONSTRUCTION METHOD OF A-OPTIMAL CHEMICAL BALANCE WEIGHING DESIGNS

Here, we study the design in that we determine unknown measurements of p objects by used of n measurement operations. For that reason we consider the chemical balance weighing design under assumption that the measurement errors are uncorrelated and they have the same variances. We give new construction method of the A-optimal chemical balance weighing design based on the incidence matrices of the balanced bipartite weighing designs and the ternary balanced block designs. The consequence of the proposed method is widening of possible classes in that A-optimal design exists