DOE design generator builds the run sheet for a designed experiment — full factorial 2^k, regular fractional factorial 2^(k−p), central composite (CCD), or Box-Behnken — with optional center points and a reproducibly randomized run order. It creates the design; it does not analyze data.
A two-level full factorial 2^k covers every high/low combination, so all main effects and interactions are estimable with no aliasing. When k is large this gets expensive, so a regular fractional factorial 2^(k−p) runs a carefully chosen 1/2^p share: the last p factors are assigned to interaction columns of the basic factors (the generators), which deliberately confounds (aliases) high-order interactions with lower-order effects. The defining relation (the generator products over GF(2)) fixes the complete alias structure, and the design's resolution — the length of its shortest defining word — summarizes how severe the aliasing is (III: main effects aliased with two-factor interactions; IV: main effects clear of two-factor interactions but two-factor interactions aliased with each other; V: both clear).
For response-surface work (fitting curvature), central composite designs add axial (star) points at distance α from the center to a two-level factorial core: α = (2^k)^¼ gives a rotatable design (equal prediction variance at equal distance from center), while α = 1 gives a face-centered design usable when factor levels cannot be extended. Box-Behnken designs are an economical three-level alternative that place points at the midpoints of the design-space edges, never at the extreme corners.
Running the experiment in a randomized order guards against unknown time trends; the generator can shuffle the run order reproducibly from a seed.
Design type + number of factors (+ optional factor names); for fractional designs the fraction p; for CCD the axial-distance convention; optional center-point count; optional randomization seed.
Design metadata (run counts, resolution, defining relation, generators, complete alias structure, axial α) and the coded run matrix (run order, standard order, point type, factor settings), which can be written to the sheet to collect responses.
Read the resolution and alias structure before committing: a resolution III screen cannot separate main effects from two-factor interactions. Analyze the collected responses with the 2^k factorial DOE analysis (or a response-surface regression for CCD/Box-Behnken).