Orthogonal field

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Orthogonal fields are tables that are used in the context of statistical test planning to create test designs.

application

The orthogonal field ${\displaystyle L_{8}(2^{3})}$

The simplest and most commonly used orthogonal fields contain rows and columns. Each field in the table has a plus or a minus. A trial factor can be assigned to each of the columns. Plus and minus stand for the two examined levels of the factor (example: factor temperature; "+" then stands for the high temperature value, "-" for the low one). The lines correspond to the test runs and indicate which of its two levels each of the factors in the relevant test run must be placed on. ${\displaystyle 2^{n}}$ ${\displaystyle 2^{n}-1}$

Sometimes numbers (1, 2 or, for three factor levels, e.g. -, 0, + or 1, 2, 3) are used instead of coding with - and +.

Orthogonal fields are of central importance in the Taguchi method .

Mathematical backgrounds

Orthogonal arrays are such that the main effects of the factors examined not another mixed be. The reason is that the scalar product of any two columns is always 0, so the plus and minus signs in the column pairs are always evenly distributed and balanced against each other.

Orthogonal fields have abbreviations such as As , , , etc. The stands for Latin square . ${\displaystyle L_{8}}$ ${\displaystyle L_{16}}$ ${\displaystyle L_{32}}$ ${\displaystyle L_{64}}$ ${\displaystyle L}$

Web links

• Orthogonal Arrays (Taguchi Designs) , York University website