Widely Used DOE Frameworks

1. Classical DOE (Fisherian DOE)

These are foundational experimental designs used for screening, modeling, and optimization.

Key Methods

• Full Factorial Designs
  Explore all combinations of factors and levels; gold standard for interaction analysis.
• Fractional Factorial Designs
  Reduced version of full factorials; efficient for screening many factors.
• Randomized Block Designs
  Control nuisance variables by grouping similar experimental units.
• Latin Square / Graeco‑Latin Square Designs
  Control two or more blocking factors simultaneously.

2. Taguchi Method (Robust Design)

Focuses on robustness and minimizing variation due to noise factors.

Key Methods

• Orthogonal Arrays (OA)
  Highly efficient designs for screening and robustness evaluation.
• Signal‑to‑Noise (S/N) Ratios
  Optimize for robustness rather than mean performance alone.
• Taguchi Loss Function
  Quantifies quality loss as deviation from target.

3. Response Surface Methodology (RSM)

Used for modeling curvature and finding true optima in continuous processes.

Key Methods

• Central Composite Design (CCD)
  Most common RSM design; includes factorial points, axial points, and center points.
• Box–Behnken Design (BBD)
  Efficient RSM design without extreme corner points.
• Second‑Order Polynomial Modeling
  Fits curvature and interactions for optimization.

4. Sequential / Adaptive DOE

Used when experiments are expensive or when models must be refined iteratively.

Key Methods

• Sequential RSM
  Start with screening → move to RSM → refine near optimum.
• Adaptive Sampling / Active Learning
  Choose next experiment based on model uncertainty.
• Bayesian Optimization (BO)
  Uses probabilistic surrogate models (e.g., Gaussian Processes).

5. Mixture Designs

Used when factors are proportions of a mixture (e.g., chemicals, materials).

Key Methods

• Simplex‑Lattice Designs
  Systematic exploration of mixture proportions.
• Simplex‑Centroid Designs
  Efficient for modeling interactions in mixtures.
• Scheffé Polynomial Models
  Specialized regression models for mixture constraints.

6. Optimal Designs (Computer‑Generated DOE)

Used when classical designs are infeasible due to constraints.

Key Methods

• D‑Optimal Designs
  Maximize information content of the design matrix.
• A‑Optimal / G‑Optimal Designs
  Minimize prediction variance or maximize worst‑case performance.
• Custom Designs
  Generated by software (JMP, Minitab, Design‑Expert) for constrained spaces.

7. Robust Optimization & Tolerance Design

Used to optimize both mean performance and variability.

Key Methods

• Dual Response Surface Method
  Separate models for mean and variance.
• Noise Factor Modeling
  Explicitly incorporate environmental or process noise.
• Monte‑Carlo‑Enhanced DOE
  Combine DOE with simulation for variability analysis.

8. DOE for Machine Learning / High‑Dimensional Systems

Modern approaches for complex engineering systems.

Key Methods

• Latin Hypercube Sampling (LHS)
  Space‑filling design for simulation and ML training.
• Sobol Sequences / Quasi‑Random Designs
  Uniform coverage of high‑dimensional spaces.
• Designs for Surrogate Modeling
  DOE tailored for neural networks, GPs, or ensemble models.

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