Response Surface Methods (RSM)

Response Surface Methodology (RSM) extends factorial experiments to locate the optimum settings of continuous factors by fitting a quadratic (curved) model to the response surface.

When to use RSM

Use RSM after a screening DOE (e.g., fractional factorial) has identified the key factors. RSM characterizes the curvature of the response and finds the maximum, minimum, or saddle point of the response surface.

Central Composite Design (CCD)

CCD adds axial (star) points at ±α and center points to a 2ᵏ factorial. For k = 2 factors: 2² = 4 factorial points: (±1, ±1) 4 axial points: (±α, 0), (0, ±α) Center points: (0, 0) × n_c Total runs = 4 + 4 + n_c α = 1.414 for rotatability (face-centered: α = 1)

Box-Behnken design

An alternative to CCD that avoids runs at the extreme corners of the factor space (all factors at high or low simultaneously). Useful when corner conditions are dangerous or impractical.

Fitted quadratic model

ŷ = β₀ + β₁x₁ + β₂x₂ + β₁₁x₁² + β₂₂x₂² + β₁₂x₁x₂

CQE exam tips

RSM requires significantly more runs than screening designs — it is used after factors are identified.
Contour plots and 3D surface plots visualize the response surface and help identify the optimal region.
Desirability functions allow simultaneous optimization of multiple responses.

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