tradeOffTable: A trade-off table of fractional factorial designs
Description
Creates a new plot that shows a trade-off table for fractional factorial designs.
Usage
tradeOffTable()Arguments
Author
Kevin Dunn, <kgdunn@gmail.com>
Details
Displays the following trade-off table:
The rows in the table are the number of experiments done in the fractional factorial (\(n\)).
The columns are the number of factors under investigation in the design (\(k\)).
The cell at a particular row/column intersection gives several pieces of information:
The top-left entry of the form: \(2^{k-p}=n\). For example, \(p=1\) corresponds to half-fractions, and \(p=2\) corresponds to quarter-fractions.
The subscript in the top-left entry, written in Roman numerals gives the design resolution. For example, \(IV\) corresponds to a resolution 4 design, implying 2-factor interactions are at most confounded with other 2-factor interactions.
The bold entries in the bottom-right tell how to generate the remaining factors in the design.
A "full" entry indicates a full factorial; while "twice" indicates a twice replicated full factorial.
Blank entries are impossible fractional factorial combinations.
A detailed explanation of the table is provided in the book reference.
References
Chapter 5 of the following book: Kevin Dunn, 2010 to 2026, Process Improvement using Data, https://learnche.org/pid/
Please see this paper to gain an understanding of how these trade-off tables are constructed:
Arthur Fries and William G. Hunter, (1980) Minimum Aberration \(2^{k-p}\) Designs, Technometrics, 22(4), pp. 601-608, https://www.jstor.org/stable/1268198
See Also
tradeoff which can be used to extend the table out to more factors or more experiments.