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Taguchi How-To

This walkthrough builds an L9 Taguchi array for four three-level factors, and shows the one thing about this design type that trips people up: what the design sheet records is not always what you chose.

Nothing here needs data. A design is built before the experiment is run, so every number below is determined by the design itself and you can check each one against your own sheet.

Steps

  1. QXL DOE New > Create Design, choose Taguchi, press Next.

  2. On Select design type choose 3-Level Design (2 -13 factors).

  3. Set Number of Factors: to 4. The Number of runs: list offers the arrays that can hold four three-level factors; choose L9.

  4. Name the four factors and their three levels each, name one output, and press Finish.

What you get

Nine runs for four factors, where a full three-level factorial would need 81.

The L9 array holds exactly four columns, so four factors fill it completely.

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

In coded units the nine runs are:

Press Copy for Excel and paste the block into an empty part of the worksheet to compare it against your sheet. The three coded levels stand for each factor's first, second and third level in the order you named them.

Run A B C D
1 -1 -1 -1 -1
2 -1 0 0 0
3 -1 +1 +1 +1
4 0 -1 0 +1
5 0 0 +1 -1
6 0 +1 -1 0
7 +1 -1 +1 0
8 +1 0 -1 +1
9 +1 +1 0 -1

Every column is balanced: each factor takes each of its three levels on exactly three runs. Add any column up and it comes to zero.

Every PAIR of columns is balanced too, which is the stronger property and the one that makes the array orthogonal rather than merely tidy: take any two columns and each of the nine possible level combinations appears exactly once. That is what lets each main effect be estimated from a fair comparison, and it is the whole construction of the array.

The trap: the sheet names the array's largest split

Build an L18 with 1 two-level and 3 three-level factors and the sheet still records it as L18 (1 two-level and 7 three-level factors array). The line names the array's largest split, not the entry you chose in the list, so the sheet and your choice can disagree.

Count the factor columns on the sheet if you need to know what was actually built. The columns are what you asked for; the array name beside them is the array's full capacity.

What this design estimates

Main effects, in the run counts above. An L9 spends its eight degrees of freedom on four factors at two each, so there is nothing left for an interaction. As with a Plackett-Burman design, treat a large effect as a signal worth following up rather than as a coefficient you can quote.

Things to try next

  • Choose Mixed 2-Level and 3-Level design (2 -26 factors) and watch the Number of runs: list change to the mixed arrays.
  • Ask for 5 factors on a 3-Level Design. L9 holds only four columns, so the next array up is offered.
  • Build the same four factors as a full three-level factorial. 81 runs against 9, and every interaction becomes estimable, which is exactly the trade this array makes.

See Also