Discussiones Mathematicae Probability and Statistics 21(2) (2001) 111-120

Bronisław Ceranka and Małgorzata Graczyk

*Department of Mathematical and Statistical Methods
Agricultural University of Poznań
Wojska Polskiego 28, 60-637 Poznań, Poland*

**Keywords:** chemical balance weighing design, ternary balanced block design.

**2000 Mathematics Subject Classification:** 62K15.

[1] | K.S. Banerjee, Weighing Designs for Chemistry, Medicine, Economics, Operations
Research, Statistics, Marcel Dekker Inc., New York 1975. |

[2] | E.J. Billington, Balanced n-array designs: a combinatorial survey and some new results,
Ars Combinatoria 17 A (1984), 37-72. |

[3] | E.J. Billington and P.J. Robinson, A list of balanced ternary designs with r ≤ 15, and some necessary existence conditions, Ars Combinatoria 16 (1983),
235-258. |

[4] | B. Ceranka and K. Katulska, Chemical balance weighing designs under the restriction on
the number of objects placed on the pans, Tatra Mt. Math. Publ., 17 (1999), 141-148. |

[5] | B. Ceranka, K. Katulska and D. Mizera,The application of ternary balanced block designs
to chemical balance weighing designs, Discuss. Math. Algebra and Stochastic Methods 18 (1998),
179-185. |

[6] | H. Hotelling, Some improvements in weighing and other experimental techniques, Ann.
Math. Stat., 15 (1944), 297-305. |

[7] | D. Raghavarao, Constructions and Combinatorial Problems in Designs of Experiments,
John Wiley Inc., New York 1971. |

[8] | C.R. Rao, Linear Statistical Inference and its Applications, Second Edition, John
Wiley Inc., New York 1973. |

[9] | M.N. Swamy, Use of balanced bipartite weighing designs as chemical balance designs,
Comm. Statist. Theory Methods 11 (1982), 769-785. |

Received 12 December 2001