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Taguchi Designs¶

QXL DOE New > Create Design > Screening > Create Taguchi Design

Taguchi designs are named orthogonal arrays. You choose the array, and the array fixes the run count and how many factors of each level count it can hold.

Choosing the design¶

The page is headed Select Taguchi design and starts with Select design type, three choices that filter the array list:

Choice	Factors it covers
2-Level Design (2 -31 factors)	every factor at two levels
3-Level Design (2 -13 factors)	every factor at three levels
Mixed 2-Level and 3-Level design (2 -26 factors)	some factors at two levels and some at three

Then Number of Factors: and Number of runs: narrow it to an array.

The arrays¶

The array name gives the run count. A mixed array's shape is spelled out rather than encoded: the Number of runs: list offers entries such as L18 - 1 two-level and 7 three-level factors, and the design sheet records the array in the same style, as L18 (1 two-level and 7 three-level factors array).

The line on the sheet always names the array's largest split, not the one you picked. An L18 built with 1 two-level and 3 three-level factors still records itself as L18 (1 two-level and 7 three-level factors array), so the sheet and the entry you chose in the list can disagree. Count the factor columns on the sheet if you need to know what was actually built.

Array	Runs	Levels	Factors it can hold
L4	4	2	3
L8	8	2	7
L9	9	3	4
L12	12	2	11
L16	16	2	15
L18	18	mixed	1 two-level plus 1 to 7 three-level
L27	27	3	13
L32	32	2	see the design type ranges above
L36, first form	36	mixed	1 to 11 two-level plus 1 to 12 three-level
L36, second form	36	mixed	1 to 3 two-level plus 13 three-level
L54	54	mixed	1 two-level plus 3 to 25 three-level

Note there are two different 36-run arrays, with different mixes, so the run count alone does not identify the design.

The mixed arrays hold a range of factors, not one fixed split, which is why four of the rows above give a range. Number of runs: lists one entry per split that will hold the factor count you asked for, so a single Number of Factors: value usually produces several entries, sometimes from more than one array. Asking for four mixed factors, for example, offers an L18 with 1 two-level and 3 three-level, three different L36 splits, and an L54, as five separate choices. Read the whole entry rather than just the array name, because the split is the part that differs.

Each mixed array also has a smallest and largest total it will accept, which is why the ranges above do not tell you the whole story on their own: 2 to 8 factors for the L18, 3 to 23 for the first 36-run form, 14 to 16 for the second, and 4 to 26 for the L54. The second 36-run form therefore never appears below 14 factors, whatever its two-level range suggests.

Four of the arrays are built from a full factorial, L4, L8, L16 and L32. On those four, the Array column list on the Factors page names the term each column carries, in brackets after the number, for example 3 (AB). For every other array the list shows bare column numbers.

That is a property of the dropdown, not of the sheet. Every Taguchi design sheet names its array, in a line such as L8 (7 two-level factors array).

Factors¶

The second page is headed Factors and is the Taguchi version of the factor page: one row per factor, under a heading strip reading, from the left, Lev., Input name, Categorical, Range and Array column.

A quantitative factor's row shows Low: and High: for its range, and nothing else. Its level count, 2 or 3, is the plain bold number at the left of the row, under the Lev. heading, which every row carries whatever its type.

A categorical factor's row replaces Low: and High: with a Levels: label and one box per level for typing the level names. So Levels: belongs to the categorical layout and is not a count. This layout is used by the Taguchi pages only; no other design type has it.

You choose which array column each factor is assigned to, from the Array column list on its row, and no two factors may share a column. Trying to finish with a duplicate is refused with Array columns must be unique., and the page scrolls to the offending row.

A factor is either Quantitative or Categorical, and the choice changes what the software can do with it.

A Quantitative factor takes numeric values on a scale, so the model can interpolate between the settings you ran and predict at a value you did not run. It is coded to a common scale before the regression, and it can carry an axis on a surface or contour chart.

A Categorical factor takes named levels with no scale between them. It is never coded to a numeric range; instead each non-reference level gets its own coefficient. There is nothing between two levels to predict at, so a chart that needs to evaluate the model between settings either refuses a categorical factor on that axis or draws it as separate levels rather than as a line. Which of the two depends on the chart, and each chart page says.

Center points¶

Taguchi designs get no center points, and Modify Design > Add/Remove Center Points refuses with center points are not available for the Taguchi design.

The page sequence¶

Select Taguchi design > Factors > Define outputs (responses) > Enter number of replicates and number of blocks.