tradeOffTable: A trade-off table of fractional factorial designs
In pid: Process Improvement using Data

Description Usage Details Value Note Author(s) References See Also Examples

Creates a new plot that shows a trade-off table for fractional factorial designs.

1	tradeOffTable()

Displays the following trade-off table:

Figure: DOE-trade-off-table.png

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.

Create a new plot displaying the trade-off table.

Certain blocks are not unique. For example, a 2^{8-3} resolution IV design (with 32 runs and 8 factors) is shown as having +/-F = ABC, +/-G=ABD and +/-H=ACDE. But another option is +/-H=BCDE, which you might see in other software, or tables in textbooks.

Kevin Dunn, <kgdunn@gmail.com>

Chapter 5 of the following book: Kevin Dunn, 2010 to 2019, 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

tradeoff which can be used to extend the table out to more factors or more experiments.