Design of Experiments

Taguchi L18 (2¹·3⁷, Mixed-Level Array)

Orthogonal array with 18 runs and one 2-level plus seven 3-level columns — the classic mixed-level screening design.

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Description

L18 is one of the key Taguchi mixed-level arrays: 18 runs covering up to eight factors, of which one is 2-level and up to seven are 3-level. Practical use: a binary factor (supplier old/new, tool A/B) plus several 3-level process parameters (low/mid/high). In D.Mike's design planner, L18 is auto-selected as soon as the factor mix matches its level structure; factor-to-column assignment is by level count. Per column, the correct level count is used for coding: ±1 for the 2-level column, −1/0/+1 for the 3-level columns — in the same row.

Formulas

Level structure

L18 : 2^{1} \cdot 3^{7} = col 0 [2, cols 1-7 3, 3, 3, 3, 3, 3, 3]

Column 0 has 2 levels; columns 1–7 each have 3 levels

Run-count

N = 18 (unabh \overset{a}{¨} ngig von der genutzten Faktor-Anzahl)

Constant 18 runs regardless of how many of the up-to-8 columns are used

Per-column coding

v \in {0, 1, \dots, n_{j} - 1} \to - 1 + \frac{2 v}{n _{j} - 1}

Column j with n_j levels maps evenly-spaced to [-1, +1]

Assumptions

Exactly 1 factor with 2 levels plus 1–7 factors with 3 levels
Linear or main-effects model — L18 cannot estimate interactions

Limitations

Interactions are confounded with main effects in L18; for interaction estimation prefer D-optimal or full factorial
Exactly one 2-level factor — two or more 2-level factors don't fit L18

References

Taguchi, G. (1987). System of Experimental Design, UNIPUB/Kraus
Phadke, M.S. (1989). Quality Engineering Using Robust Design, Prentice Hall — Chapter 6 (Mixed-Level Orthogonal Arrays)