On certain A-optimal chemical balance weighing designs

Highly D‑efficient Weighing Design and Its Construction

“…The problems of optimality of spring balance weighing designs under different assumptions concerning the measurement error are discussed in the literature, see Masaro and Wong (2008a;2008b), Ceranka and Graczyk (2014a;2014b;2014c). Unfortunately, the properties of experimental designs and the relations between their parameters are the reasons why we are not able to determine the optimal design in any class Φ n×p (0, 1).…”

“…Any spring balance weighing design is defined as a design in which we determine unknown measurements of p objects in n measurement operations according to the model y = Xw + e, where: 1) y is a n × 1 random vector of the recorded results of measurements, 2) X = (x ij ) ϵ Φ n×p (0, 1), Φ n×p (0, 1) denotes the class of matrices with elements x ij = 1 or 0, i = 1, 2, …, n, j = 1, 2, …, p, 3) w is a p × 1 vector of unknown measurements of objects, 4) e is an n × 1 random vector of errors, E(e) = 0 n and E(ee') = σ 2 G, G is known as a positive definite matrix. The possibility of using the proposed methodology of measuring economic phenomena is presented in Banerjee (1975) and Ceranka and Graczyk (2014c).…”

D-optimal and highly D-efficient designs with non-negatively correlated observations

“…Katulska and Smaga [22] constructed D*-optimal designs for certain n and p using Hadamard matrices. That construction is also the construction of A-optimal designs considered in Ceranka et al [8].…”

On D-Optimal Chemical Balance Weighing Designs

“…Originally, the name chemical balance weighing design pertained to experiments connected with determining of unknown weights of objects by use of balance with two pans which is called chemical balance. Nowadays, such designs are applied in many branches of knowledge including economic survey, see Banerjee (1975), Ceranka and Graczyk (2014). Some aspects of the other applications of the chemical balance weighing designs are presented in Koukouvinos and Seberry (1997), Graczyk (2013), Katulska and Smaga (2013).…”