Nearly Resolution V Plans on Blocks of Small Size

In the present paper we aim at constructing plans (designs) for symmetrical experiments on small blocks such that factorial effects (main effects or interactions) are ‘orthogonal through the block factor’. Specifically, given an initial plan, we derive sufficient conditions on the set of ‘generators...

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Veröffentlicht in:Journal of statistical theory and practice Jg. 14; H. 1
1. Verfasser: Bagchi, Sunanda
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Cham Springer International Publishing 01.03.2020
Schlagworte:
Algorithms
Analysis and Advanced Methodologies in the Design of Experiments
Mathematics and Statistics
Original Article
Probability Theory and Stochastic Processes
Statistical Theory and Methods
Statistics
Symmetrical experiment
Two-factor interaction
Orthogonality through the block factor
ISSN:1559-8608, 1559-8616
Online-Zugang:Volltext
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Beschreibung
Zusammenfassung:In the present paper we aim at constructing plans (designs) for symmetrical experiments on small blocks such that factorial effects (main effects or interactions) are ‘orthogonal through the block factor’. Specifically, given an initial plan, we derive sufficient conditions on the set of ‘generators’ for a desired change in the relation between a pair of factorial effects in the generated plan—non-orthogonality turning to orthogonality and aliased effects turn into non-aliased. We illustrate the theory with plans for two- and three-level factors on blocks of size four or less, estimating main effects as well as two-factor interactions. The plans constructed have the following features. They are inter-class orthogonal, in the sense that each effect of interest is orthogonal to all effects except the ones in its own class. The sizes of the classes are small, so that amount of non-orthogonality is limited. In particular, in the plans for experiments with three-level factors, most of the main effects are orthogonal to all others.
ISSN:1559-8608
1559-8616
DOI:10.1007/s42519-019-0074-3