A Highly D‑efficient Spring Balance Weighing Design for an Even Number of Objects

Authors

DOI:

https://doi.org/10.18778/0208-6018.344.02

Keywords:

highly D-efficient design, spring balance weighing design

Abstract

The problem of determining unknown measurements of objects in the model of spring balance weighing designs is presented. These designs are considered under the assumption that experimental errors are uncorrelated and that they have the same variances. The relations between the parameters of weighing designs are deliberated from the point of view of optimality criteria. In the paper, designs in which the product of the variances of estimators is possibly the smallest one, i.e. D‑optimal designs, are studied. A highly D‑efficient design in classes in which a D‑optimal design does not exist are determined. The necessary and sufficient conditions under which a highly efficient design exists and methods of its construction, along with relevant examples, are introduced.

Downloads

Download data is not yet available.

References

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

Beckman R. J. (1973), An applications of multivariate weighing designs, “Communication in Statistics”, no. 1(6), pp. 561–565.
Google Scholar

Bulutoglu D. A., Ryan K. J. (2009), D‑optimal and near D‑optimal 2k fractional factorial designs of resolution V, “Journal of Statistical Planning and Inference”, no. 139, pp. 16–22.
Google Scholar

Ceranka B., Graczyk M. (2014), The problem of D‑optimality in some experimental designs, “International Journal of Mathematics and Computer Application Research”, no. 4, pp. 11–18.
Google Scholar

Ceranka B., Graczyk M. (2018), Highly D‑efficient designs for even number of objects, “REVSTAT‑Statistical Journal”, no. 16, pp. 475–486.
Google Scholar

Ceranka B., Graczyk M. (2019), Recent developments in D‑optimal designs. Communication in Statistics – Theory and Methods, Accepted to publication.
Google Scholar

Ceranka B., Katulska K. (1987), Zastosowanie optymalnych sprężynowych układów wagowych, “Siedemnaste Colloquium Metodologiczne z Agro‑Biometrii”, PAN, pp. 98–108.
Google Scholar

Harville D. A. (1997), Matrix Algebra from a Statistician’s Point of Perspective, Springer‑Verlag, New York.
Google Scholar

Jacroux M., Notz W. (1983), On the optimality of spring balance weighing designs, “The Annals of Statistics”, no. 11(3), pp. 970–978.
Google Scholar

Jacroux M., Wong C. S., Masaro J. C. (1983), On the optimality of chemical balance weighing design, “Journal of Statistical Planning and Inference”, no. 8, pp. 213–240.
Google Scholar

Masaro J., Wong C. S. (2008a), Robustness of A‑optimal designs, “Linear Algebra and its Applications”, no. 429, pp. 1392–1408.
Google Scholar

Masaro J., Wong C. S. (2008b), D‑optimal designs for correlated random errors, “Journal of Statistical Planning and Inference”, no. 130, pp. 4093–4106.
Google Scholar

Neubauer M. G., Watkins S., Zeitlin J. (1997), Maximal j‑simplices in the real d‑dimensional unit cube, “Journal of Combinatorial Theory”, Ser. A 80, pp. 1–12.
Google Scholar

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

Shah K. R., Sinha B. K. (1989), Theory of Optimal Designs, Springer‑Verlag, Berlin.
Google Scholar

Downloads

Published

2019-09-30

How to Cite

Graczyk, M., & Ceranka, B. (2019). A Highly D‑efficient Spring Balance Weighing Design for an Even Number of Objects. Acta Universitatis Lodziensis. Folia Oeconomica, 5(344), 17–27. https://doi.org/10.18778/0208-6018.344.02

Issue

Section

Articles

Most read articles by the same author(s)

1 2 > >> 

Similar Articles

<< < 1 2 3 4 5 6 7 > >> 

You may also start an advanced similarity search for this article.