Design of Experiments

DoE Planner (Design Generation)

Generates structural experimental designs: full 2^k, fractional 2^(k-p), CCD and Box-Behnken.

Statusvalidated

Version1.0.0

Minitab equivalentStat > DOE > Factorial / Response Surface > Create Design

Description

The DoE planner generates the four standard experimental designs most used in Six Sigma: full 2^k factorial, fractional 2^(k-p) (with lossless lookup tables for the classic generator columns from the DoE literature), central composite design (rotatable / spherical / face-centered with axial and center points), and Box-Behnken (for k = 3–7). The analyze() dispatcher returns only the structural properties — runCount, factorCount, resolution, codedMatrix and (for CCD) alpha — making it the ideal entry point for 1:1 comparison against reference values. Randomisation and the conversion from coded to actual factor levels are handled by the full planner function generateDesign(factors, opts).

Formulas

Full 2^k

N = 2^{k}

Number of runs in a full factorial

Fraktioniert

N = 2^{k - p}

Number of runs in a 2^(k-p) fraction; p = number of generator columns

CCD Runs

N_{CCD} = 2^{k} + 2 k + n_{c}

Factorial + axial + center runs of a CCD

CCD α

α_{rotatable} = (2^{k})^{1/4}, α_{spherical} = k, α_{face-centered} = 1

Axial point distance for the three CCD variants

Box-Behnken Runs

N_{BB} = 4 (2 k)_{(pair template)} + n_{c}

Edge runs from the BB pair template plus center points

Assumptions

Factor levels are coded -1 (low), 0 (center), +1 (high) — CCD additionally ±α
Row order follows the MSB-first Yates convention (no randomisation)

Limitations

Fractional generator tables cover up to 2^(8-4)
Box-Behnken only supported for k = 3–7
analyze() ignores randomisation and actual factor levels — use generateDesign() for that

References

Montgomery, Design and Analysis of Experiments, 10th Ed. — Chapters 6, 8, 11
Box, G. E. P. & Behnken, D. W. (1960), Some New Three Level Designs for the Study of Quantitative Variables, Technometrics, 2(4), 455–475
Box, G. E. P. & Wilson, K. B. (1951), On the Experimental Attainment of Optimum Conditions, JRSS B, 13(1), 1–45