Title: Uniformity of incomplete block designs

Authors: Min-Qian Liu, Ling-Yau Chan

Addresses: Department of Statistics, Nankai University, Tianjin 300071, People's Republic of China. ' Department of Industrial and Manufacturing Systems Engineering, The University of Hong Kong, Pokfulam Road, Hong Kong

Abstract: Incomplete block designs are a type of experimental design layout that has had widespread use in science and engineering. A balanced incomplete block design (BIB) can be characterised by the balanced arrangement of its design points. In this article, incomplete block designs will be investigated from a new perspective: the perspective of uniformity in distribution of design points. A design is of high uniformity, or low discrepancy, if its design points distribute uniformly over the entire design space. The authors use a general discrepancy measure to prove theoretically that BIBs are the most uniform ones among all binary incomplete block designs.

Keywords: balanced incomplete block design; uniformity; uniform design; discrepancy.

DOI: 10.1504/IJMPT.2004.003918

International Journal of Materials and Product Technology, 2004 Vol.20 No.1/2/3, pp.143 - 149

Published online: 10 May 2004 *

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