| Title:
|
Optimal chemical balance weighing designs for $v+1$ objects (English) |
| Author:
|
Ceranka, Bronisław |
| Author:
|
Graczyk, Małgorzata |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
39 |
| Issue:
|
3 |
| Year:
|
2003 |
| Pages:
|
[333]-340 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The paper studies the estimation problem of individual weights of objects using a chemical balance weighing design under the restriction on the number times in which each object is weighed. Conditions under which the existence of an optimum chemical balance weighing design for $p = v$ objects implies the existence of an optimum chemical balance weighing design for $p = v + 1$ objects are given. The existence of an optimum chemical balance weighing design for $p = v + 1$ objects implies the existence of an optimum chemical balance weighing design for each $p < v + 1$. The new construction method for optimum chemical balance weighing design for $p = v + 1$ objects is given. It uses the incidence matrices of ternary balanced block designs for v treatments. (English) |
| Keyword:
|
chemical balance weighing design |
| Keyword:
|
ternary balanced block design |
| MSC:
|
62K05 |
| MSC:
|
62K10 |
| MSC:
|
62K15 |
| MSC:
|
92E20 |
| idZBL:
|
Zbl 1248.62128 |
| idMR:
|
MR1995737 |
| . |
| Date available:
|
2009-09-24T19:54:24Z |
| Last updated:
|
2015-03-23 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/135535 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
[3] Billington E. J., Robinson P. J.: A list of balanced ternary block designs with $r \le 15$ and some necessary existence conditions.Ars Combin. 16 (1983), 235–258 MR 0734059 |
| Reference:
|
[4] Ceranka B., Graczyk M.: Optimum chemical balance weighing designs under the restriction on weighings.Discuss. Math. 21 (2001), 111–120 MR 1961022, 10.7151/dmps.1024 |
| Reference:
|
[5] Ceranka B., Katulska K.: On some optimum chemical balance weighing designs for $v+1$ objects.J. Japan Statist. Soc. 18 (1988), 47–50 Zbl 0651.62072, MR 0959679 |
| Reference:
|
[6] Ceranka B., Katulska K.: Chemical balance weighing designs under the restriction on the number of objects placed on the pans.Tatra Mt. Math. Publ. 17 (1999), 141–148 Zbl 0988.62047, MR 1737701 |
| Reference:
|
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| Reference:
|
[8] Hotelling H.: Some improvements in weighing and other experimental techniques.Ann. Math. Statist. 15 (1944), 297–305 Zbl 0063.02076, MR 0010951, 10.1214/aoms/1177731236 |
| Reference:
|
[9] Raghavarao D.: Constructions and Combinatorial Problems in Designs of Experiments.Wiley, New York 1971 MR 0365935 |
| Reference:
|
[10] Saha G. M., Kageyama S.: Balanced arrays and weighing designs.Austral. J. Statist. 26 (1984), 119–124 Zbl 0599.62089, MR 0766612, 10.1111/j.1467-842X.1984.tb01225.x |
| Reference:
|
[11] Shah K. R., Sinha B. L.: Theory of Optimal Designs.Springer, Berlin 1989 Zbl 0688.62043, MR 1016151 |
| Reference:
|
[12] Swamy M. N.: Use of balanced bipartite weighing designs as chemical balance designs.Comm. Statist. Theory Methods 11 (1982), 769–785 Zbl 0514.62086, MR 0651611, 10.1080/03610928208828270 |
| . |
