Estimation of Unknown Object Measures in a Chemical Weighing Design with Correlated Errors

Małgorzata Graczyk; Bronisław Ceranka

doi:10.18778/0208-6018.368.02

Authors

Małgorzata Graczyk Poznań University of Life Sciences, Faculty of Agronomy and Bioengineering, Department of Mathematical and Statistical Methods, Poznań, Poland https://orcid.org/0000-0002-5550-7007
Bronisław Ceranka Poznań University of Life Sciences, Faculty of Agronomy and Bioengineering, Department of Mathematical and Statistical Methods, Poznań, Poland https://orcid.org/0000-0002-5395-1593

DOI:

https://doi.org/10.18778/0208-6018.368.02

Keywords:

chemical balance weighing design, D-efficient design, D-optimal design

Abstract

In this paper, some problems that concern the determining of unknown measurements of objects in the model of a chemical balance weighing design are presented. These designs are tested under the assumption that measurement errors are correlated and have the same variances. The relations between the parameters of a weighing design are considered from the point of view of the D-optimality criterion. We give some conditions determining the dependencies between the parameters of such designs and construction examples.

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References

Banerjee K.S. (1975), Weighing Designs for Chemistry, Medicine, Economics, Operation Research, Statistics, Marcell Dekker Inc., New York.

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”, vol. 139, pp. 16–22. DOI: https://doi.org/10.1016/j.jspi.2008.05.012

Ceranka B., Graczyk M. (2010), Some construction of optimum weighing designs, “Acta Universitatis Lodziensis. Folia Oeconomica”, vol. 235, pp. 235–239.

Ceranka B., Graczyk M. (2012), Notes on the optimum chemical balance weighing designs, “Acta Universitatis Lodziensis. Folia Oeconomica”, vol. 269, pp. 91–101.

Ceranka B., Graczyk M. (2019), Recent developments in D‑optimal designs, “Communications in Statistics – Theory and Methods”, vol. 48(6), pp. 1470–1480, https://doi.org/10.1080/03610926.2018.1433851 DOI: https://doi.org/10.1080/03610926.2018.1433851

Gail Z., Kiefer J. (1982), Construction methods for D‑optimum weighing designs when n ≡ 3 mod 4, “The Annals of Statistics”, vol. 10, pp. 502–510. DOI: https://doi.org/10.1214/aos/1176345791

Gawande B.N., Patkar A.Y. (1999), Application of factorial design for optimization of Cyclodextrin Glycosyltransferase production from Klebsiella Pneumoniae AS–22, “Biotechnology and Bioengineering”, vol. 64(2), pp. 168–173. DOI: https://doi.org/10.1002/(SICI)1097-0290(19990720)64:2<168::AID-BIT5>3.3.CO;2-X

Graczyk M. (2013), Some applications on weighing designs, “Biometrical Letters”, vol. 50(1), pp. 15–26. DOI: https://doi.org/10.2478/bile-2013-0014

Harville D.A. (1997), Matrix Algebra from Statistician’s Perspective, Springer–Verlag, New York. DOI: https://doi.org/10.1007/b98818

Katulska K., Smaga Ł. (2010), On some construction of D‑optimal chemical balance weighing designs, “Colloquium Biometricum”, vol. 40, pp. 37–45.

Koukouvinos Ch. (1996), Linear models and D‑optimal designs for n ≡ 2 mod 4, “Statistics and Probability Letters”, vol. 26, pp. 329–332. DOI: https://doi.org/10.1016/0167-7152(95)00028-3

Raghavarao D. (1971), Constructions and Combinatorial Problems in Designs of Experiments, John Wiley Inc., New York.Raghavarao D. (1971), Constructions and Combinatorial Problems in Designs of Experiments, John Wiley Inc., New York.

Shah K.R., Sinh B.K. (1989), Theory of Optimal Designs, Springer‑Verlag, Berlin. DOI: https://doi.org/10.1007/978-1-4612-3662-7