Orthogonal Array Design: Fractional Experiments Instead of Full Factorials
Principle of Orthogonal Arrays
An orthogonal array is a balanced experimental arrangement: every column shows each level the same number of times (balance), and every pair of columns shows each level combination the same number of times (orthogonality). With L9(3^4), 9 runs examine the main effects of four three-level factors, whereas a full factorial needs 3^4 = 81 runs. Orthogonality lets each factor's effect be estimated independently, extracting maximum information from minimum experiments.
Choosing a Common Array
L9(3^4) suits up to four three-level factors; L16 accommodates more factors or interaction columns (e.g., L16(2^15) two-level, L16(4^5) four-level); L27(3^13) suits 7-13 three-level factors. Taguchi commonly uses two-level L4/L8/L16 and three-level L9/L18/L27. The tool auto-selects the array by factor count, levels and interaction needs, proposes column assignments, and unused columns can serve as error columns.
Inner/Outer Cross-Product Design
Robust design puts control factors in the inner array and noise factors in the outer array, and runs every inner-array combination under all outer noise combinations, forming a cross-product experiment of inner rows times outer rows. The tool expands the cross-product plan automatically, labeling the control settings and noise conditions of each run so noise variation is covered systematically and each combination's robustness (S/N) can be computed. Outer-array noise levels usually take 2-3 settings spanning the real variation range; the expanded run count is the product of the two array sizes, so assess cost in advance.
How to Use It
After sign-in, select an orthogonal array, assign control factors to inner columns (the tool marks usable and interaction columns), set noise factors for the outer array, generate the cross-product plan, run it and enter data, then proceed to S/N analysis. Randomize the run order as with any DOE, and use unassigned columns to estimate error or check interactions. Confirm that every factor level is feasible and covers the actual process range before running.