New Results Regarding the Construction Method for D‑optimal Chemical Balance Weighing Designs

Authors

DOI:

https://doi.org/10.18778/0208-6018.349.08

Keywords:

balanced bipartite weighing design, balanced incomplete block design, chemical balance weighing design, D‑optimality, ternary balanced block design

Abstract

We study an experiment in which we determine unknown measurements of p objects in n weighing operations according to the model of the chemical balance weighing design. We determine a design which is D‑optimal. For the construction of the D‑optimal design, we use the incidence matrices of balance incomplete block designs, balanced bipartite weighing designs and ternary balanced block designs. We give some optimality conditions determining the relationships between the parameters of a D‑optimal design and we present a series of parameters of such designs. Based on these parameters, we will be able to set down D‑optimal designs in classes in which it was impossible so far.

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

Billington E. J. (1984), Balanced n‑array designs: a combinatorial survey and some new results, “Ars Combinatoria”, no. 17A, pp. 37–72.
Google Scholar

Ceranka B., Graczyk M. (2004a), Balanced ternary block designs under the certain condition, “Colloquium Biometricum”, no. 34, pp. 63–75.
Google Scholar

Ceranka B., Graczyk M. (2004b), Balanced bipartite weighing designs under the certain condition, “Colloquium Biometricum”, no. 34a, pp. 17–28.
Google Scholar

Ceranka B., Graczyk M. (2014), On certain A‑optimal biased spring balance weighing designs, “Statistics in Transition new series”, Spring, vol. 15(2), pp. 317–326.
Google Scholar

Ceranka B., Graczyk M. (2015), Construction method of A‑optimal chemical balance weighing designs, “Acta Universitatis Lodziensis. Folia Oeconomica”, vol. 3(314), pp. 43–51, http://doi.org/10.18778/0208-6018.314.06
Google Scholar DOI: https://doi.org/10.18778/0208-6018.314.06

Ceranka B., Graczyk M. (2016), New construction of D‑optimal weighing design with non‑negative correlations of errors, “Colloquium Biometricum”, no. 46, pp. 31–45.
Google Scholar

Ceranka B., Graczyk M. (2017), Some D‑optimal chemical balance weighing designs: theory and examples, “Biometrical Letters”, no. 54, pp. 137–154.
Google Scholar DOI: https://doi.org/10.1515/bile-2017-0008

Ceranka B., Graczyk M. (2018), Regular D‑optimal weighing design with non‑negative correlations of errors constructed from same block designs, “Colloquium Biometricum”, no. 48, pp. 1–17.
Google Scholar

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

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

Graczyk M., Janiszewska M. (2019), Remarks about construction methods about D‑optimal chemical balance weighing designs, “Biometrical Letters” [to appear].
Google Scholar DOI: https://doi.org/10.2478/bile-2019-0012

Huang Ch. (1976), Balanced bipartite block design, “Journal of Combinatorial Theory (A)”, no. 21, pp. 20–34.
Google Scholar DOI: https://doi.org/10.1016/0097-3165(76)90043-1

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 DOI: https://doi.org/10.1016/0378-3758(83)90041-1

Katulska K., Smaga Ł. (2013), A note on D‑optimal chemical balance weighing designs and their applications, “Colloquium Biometricum”, no. 43, pp. 37–45.
Google Scholar

Raghavarao D. (1971), Constructions and Combinatorial Problems in designs of Experiments, John Willey Inc., New York.
Google Scholar

Sathe Y. S., Shenoy R. G. (1990), Construction method for some A‑ and D‑optimal weighing designs when N º 3(mod 4), “Journal of Statistical Planning and Inference”, no. 24, pp. 369–375.
Google Scholar DOI: https://doi.org/10.1016/0378-3758(90)90056-Z

Downloads

Published

2020-11-23

How to Cite

Ceranka, B., & Graczyk, M. (2020). New Results Regarding the Construction Method for D‑optimal Chemical Balance Weighing Designs. Acta Universitatis Lodziensis. Folia Oeconomica, 4(349), 129–141. https://doi.org/10.18778/0208-6018.349.08

Issue

Section

Articles

Most read articles by the same author(s)

1 2 > >>