Features

Designs and analysis in detail

Everything is part of the base product — there are no add-on modules and no separately licensed extensions.

01 / Designs

The design your question calls for

Nineteen design types, no add-on module. Which one fits depends on whether you are screening factors, mapping a response surface, formulating a blend or hardening a process against noise.

Screening

Many factors, few runs

Full factorial — every level combination, 2^k and mixed-level
Fractional factorial 2^(k−p) — with alias structure and resolution III–V
Plackett-Burman — main effects in N = 8, 12, 20 or 24 runs
Definitive screening (DSD) — three levels, quadratic effects stay separable
Min-run resolution IV — equireplicated fraction, main effects clear of two-factor interactions
Min-run resolution V — same idea, interactions additionally clear of each other

Response surfaces

Mapping curvature

Central composite (CCD) — rotatable, face-centred or inscribed
Box-Behnken — three levels without corner points, when corners are infeasible or costly

When no standard design fits: optimal designs

One design type, four objectives:

D-optimal — sharpest coefficients overall
A-optimal — smallest average coefficient variance
I-optimal — smallest average prediction variance across the region
G-optimal — smallest worst prediction variance

Built by coordinate exchange, able to hold already-executed runs fixed. If a factor is hard to change, the result becomes a split-plot design with its own randomisation stratum.

Mixtures

When the parts sum to one

Simplex-lattice — {q,m} grid over the simplex
Simplex-centroid — pure components and every equal-parts blend
Extreme vertices (constrained) — vertices of the polytope that bounds cut out of the simplex, plus face centroids
Mixture: optimal — criterion-driven, when the region admits no standard lattice
Mixture × process (crossed) — formulation and processing conditions as a tensor product
Mixture-amount — when not only the ratio matters but the total amount

Robust & special

Against noise and structure

Taguchi array (L4 … L36) — orthogonal arrays, two-, three- and mixed-level
Robust parameter design (inner/outer) — control factors crossed against noise factors
Nested (hierarchical) — units within units, e.g. batch → sample → measurement
Latin hypercube — space-filling, for simulations rather than physical runs

Augment instead of starting over: an existing design can be extended — fold-over against aliasing, axial points turning a two-level design into a CCD, points for the lack-of-fit test, or a criterion-driven top-up that holds the already-executed runs fixed. That is not a design type of its own but a step on top of what you have already measured.

02 / Analysis

What becomes of the measurements

A design is half the work. The other half is deciding which effects are real, whether the model holds, where the optimum sits — and how certain any of it is.

Model & fit

Regression with ANOVA — coefficients, F tests, R², adjusted and predicted R²
Lack-of-fit test — separates model error from pure experimental error, where replicates exist
Model selection — backward elimination by AIC/BIC without breaking term hierarchy
Box-Cox — estimates the response transformation by profile likelihood, with an interval for λ
Generalized regression — ridge path against ill-conditioned model matrices, selected by AIC/AICc/BIC

Separating effects

Half-normal plot — separates real effects from noise
Pareto chart — effects by magnitude, with t and Bonferroni limits
Lenth PSE — estimates error spread from the effects themselves when no degrees of freedom remain
Two-stage DSD analysis — main effects from the fold-over space, quadratic terms from the difference space

Diagnostics & prediction

Residual analysis — studentised residuals, normal QQ, behaviour over prediction and run order
Influence diagnostics — leverage, Cook's D, DFFITS
Multicollinearity — VIF per term and the correlation matrix of the effects
Prediction with intervals — confidence interval for the mean, prediction interval for a single measurement
Confirmation runs — checks whether re-measured runs fall inside the model's prediction interval

Structure & distribution

Split-plot (REML) — its own error stratum for hard-to-change factors
Split-split-plot (REML) — three randomisation strata instead of one
Nested ANOVA — variance components of hierarchical units, via EMS and REML
Mixed models — random effects with Wald inference on the variance components
Binomial & Poisson GLM — IRLS with the canonical link, for proportions and counts
Mixture ANOVA — Scheffé models without an intercept, plus mixture traces

Optimisation & robustness

Desirability (Derringer-Suich) — several responses into one weighted overall desirability
Pareto front — shows what one objective costs the other
Profiler & ramps — every quantity on its own track; drag a factor, see the effect at once
Overlay / sweet spot — the region where every specification holds at the same time
Propagation of error (POE) — the spread a response inherits from factors that are not set exactly
Monte Carlo — distribution, defect rate and Cpk per response
Robust parameter design — S/N ratios and two-step optimisation: variance first, then the mean

Evaluating the design

Power per effect — the probability of actually detecting an effect of a given size
Replicates from power — how many replicates a target level requires
Efficiencies & prediction variance — D, A and G efficiency, FDS curves, prediction variance across the region
Strategy comparison — screen first and then refine, against one single large design

Every method follows a published standard reference cited in the source code — Montgomery, Myers, Cornell, Box & Hunter, Scheffé, Jones & Nachtsheim, McCullagh & Nelder and others.

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