On certain A-optimal biased spring  balance weighing designs

Bronisław  Ceranka; Małgorzata  Graczyk

doi:https://doi.org/10.59170/stattrans-2014-022

On certain A-optimal biased spring balance weighing designs

Bronisław Ceranka Department of Mathematical and Statistical Methods, Poznań University of Life Sciences, Wojska Polskiego 28, 60-637 Poznań, Poland. , Małgorzata Graczyk Department of Mathematical and Statistical Methods, Poznań University of Life Sciences, Wojska Polskiego 28, 60-637 Poznań, Poland. Statistics in Transition new series, vol. 15, 2014, 2, pages: 317-326 Published online: 2 June 2014 https://doi.org/10.59170/stattrans-2014-022

180 Views 9 Downloads

ARTICLE

(English) PDF

ABSTRACT

In the paper, the estimation of unknown measurements of p objects in the experiment, according to the model of the spring balance weighing design, is discussed. The weighing design is called biased if the first column of the design matrix has elements equal to one only. The A-optimal design is a design in which the trace of the inverse of information matrix is minimal. The main result is the broadening of the class of experimental designs so that we are able to determine the regular A-optimal design. We give the lowest bound of the covariance matrix of errors and the conditions under which this lowest bound is attained. Moreover, we give new construction methods of theregular A-optimal spring balance weighing design based on the incidence matrices of the balanced incomplete block designs. The example is also given.

KEYWORDS

A-optimal design, spring balance weighing design.

REFERENCES

BANERJEE, K. S., (1975). Weighing Designs for Chemistry, Medicine, Economics, Operations Research, Statistics. Marcel Dekker Inc., New York.

CERANKA, B., KATULSKA, K., (1990). Constructions of optimum biased spring balance weighing designs with diagonal covariance matrix of errors. Computational Statistics and Data Analysis 10, pp. 121–131.

CERANKA, B., KATULSKA K., (1992). Optimum biased spring balance weighing designs with non-homogeneity of the variances of errors. Journal of Statistical Planning and Inference 30, pp. 185–193.

GRACZYK, M., (2011). A-optimal biased spring balance weighing design. Kybernetika 47, pp. 893–901.

KATULSKA, K., (1989). Optimum biased spring balance weighing designs. Statistics and Probability Letters 8, pp. 267–271.

PUKELSHEIM, F., (1993). Optimal design of experiment. John Wiley and Sons. New York.

RAGHAVARAO, D., (1971). Constructions and combinatorial problems in design of experiment. John Wiley and Sons. New York.

RAGHAVARAO, D., PADGETT, L. V., (2005). Block Designs, Analysis, Combinatorics and Applications. Series of Applied Mathematics 17, Word Scientific Publishing Co. Pte. Ltd., Singapore