doe_fractional_factorial — MULTIVAR plan op

• Data kinds: none → design (an op determined by its arguments alone — it takes no image or data input)

• Call: import fullseye as fs; fs.ledger.doe_fractional_factorial(factors=5, p=2, generators=None, center=0) -> 'dict' (to call the implementation directly, import doe; doe.doe_fractional_factorial(factors=5, p=2, generators=None, center=0) -> 'dict'; from the registry, opsmultivar.get("doe_fractional_factorial"))

Usage

Regular two-level fractional factorial 2^(k-p) from generators (Box & Hunter 1961) -> design.

The first k - p factors (letters A, B, C ... skipping I) form a full factorial in standard (Yates) order, A changing fastest. Each generator "D=ABC" sets an added factor's column to the product of base columns ("E=-ABD" for the other half). generators=None takes the recommended generators for (k, p) from the NIST/SEMATECH e-Handbook table (FF_NIST, 5.3.3.4.7 Table 3.17, after Box, Hunter & Hunter); p=0 or generators=() gives the full factorial 2^k.

The defining relation (every product of generator words I = ABCD = ...), the resolution (length of the shortest word: III = main effects aliased with two-factor interactions, IV = main effects clear but 2fi aliased with each other, V = 2fi clear) and the alias table of main effects and two-factor interactions are returned in meta and alias. They are computed from the generators, and the returned matrix is checked against them (each aliased pair of columns is identical up to sign).

center adds centre runs (coded 0) for a curvature check; they do not change the alias structure.

Detailed usage guide

• design_of_experiments family guide

References (sample data, literature)

• Sample-data catalog (download URLs / licences) — 2-D uses skimage.data (BSD/public domain) plus synthetic images; 3-D lists download URLs for real data sources (Stanford, PDS, …).

• Operator provenance and references — the sources of the research/methods this op family came from.

• The canonical algorithm (author, year) and its uses are named in the family usage guide above.

Runnable examples (verified samples that actually call this op)

• doe_plan_tour — py -3.11 examples/doe_plan_tour.py

Ops the type connects to (they accept design as input)

doe_decode · rsm_fit · doe_main_effects · sens_morris · sens_sobol

Same category (plan)

doe_lhs · doe_orthogonal_array · doe_central_composite · doe_box_behnken

*Provenance: doe.py — MULTIVAR operator registry. This per-op note is generated by tools/opdocs.py md (do not hand-edit).*

© 2026 Kazufumi Furuse — Fullseye operator documentation. Licensed under Apache-2.0.