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Column Designs (column + design)

Distribution by Scientific Domains

Mathematics and Statistics	80%

Selected Abstracts

Construction of Resolvable Spatial Row,Column Designs

BIOMETRICS, Issue 1 2006
E. R. Williams
Summary Resolvable row,column designs are widely used in field trials to control variation and improve the precision of treatment comparisons. Further gains can often be made by using a spatial model or a combination of spatial and incomplete blocking components. Martin, Eccleston, and Gleeson (1993, Journal of Statistical Planning and Inference34, 433,450) presented some general principles for the construction of robust spatial block designs which were addressed by spatial designs based on the linear variance (LV) model. In this article we define the two-dimensional form of the LV model and investigate extensions of the Martin et al. principles for the construction of resolvable spatial row,column designs. The computer construction of efficient spatial designs is discussed and some comparisons made with designs constructed assuming an autoregressive variance structure. [source]

Designs for two-colour microarray experiments

JOURNAL OF THE ROYAL STATISTICAL SOCIETY: SERIES C (APPLIED STATISTICS), Issue 4 2007
R. A. Bailey
Summary., Designs for two-colour microarray experiments can be viewed as block designs with two treatments per block. Explicit formulae for the A- and D-criteria are given for the case that the number of blocks is equal to the number of treatments. These show that the A- and D-optimality criteria conflict badly if there are 10 or more treatments. A similar analysis shows that designs with one or two extra blocks perform very much better, but again there is a conflict between the two optimality criteria for moderately large numbers of treatments. It is shown that this problem can be avoided by slightly increasing the number of blocks. The two colours that are used in each block effectively turn the block design into a row,column design. There is no need to use a design in which every treatment has each colour equally often: rather, an efficient row,column design should be used. For odd replication, it is recommended that the row,column design should be based on a bipartite graph, and it is proved that the optimal such design corresponds to an optimal block design for half the number of treatments. Efficient row,column designs are given for replications 3,6. It is shown how to adapt them for experiments in which some treatments have replication only 2. [source]

Design and analysis of industrial strip-plot experiments

QUALITY AND RELIABILITY ENGINEERING INTERNATIONAL, Issue 2 2010
Heidi Arnouts
Abstract The cost of experimentation can often be reduced by forgoing complete randomization. A well-known design with restricted randomization is a split-plot design, which is commonly used in industry when some experimental factors are harder to change than others or when a two-stage production process is studied. Split-plot designs are also often used in robust product design to develop products that are insensitive to environmental or noise factors. Another, lesser known, type of experimental design plan that can be used in such situations is the strip-plot experimental design. Strip-plot designs are economically attractive in situations where the factors are hard to change and the process under investigation consists of two distinct stages, and where it is possible to apply the second stage to groups of semi-finished products from the first stage. They have a correlation structure similar to row,column designs and can be seen as special cases of split-lot designs. In this paper, we show how optimal design of experiments allows for the creation of a broad range of strip-plot designs. Copyright © 2009 John Wiley & Sons, Ltd. [source]