Definitive Screening Design

Modern three-level screening design that efficiently identifies main effects and quadratic effects while maintaining the ability to estimate some two-factor interactions.

Definitive Screening Design Overview & Bridging Screening/Optimization

What it accomplishes:

Definitive Screening Designs (DSDs) use three levels (low, center, high) with 2k+1 runs to screen k factors. They can estimate main effects, quadratic effects, and some two-factor interactions without confounding, making them ideal for bridging screening and optimization phases.

Advantages:

• • Main effects unconfounded with two-factor interactions
• • Estimates quadratic effects (curvature)
• • No confounding between quadratics and two-factor interactions
• • Model-robustness properties
• • Efficient run count (2k+1)

Considerations:

• • More runs than two-level screening
• • Not all interactions estimable simultaneously
• • Requires three-level factors
• • Model selection needed for interactions

Run Count & Second-Order Model Structure

Design Size:

Definitive screening design run count

= number of factors

= number of runs

Each factor is set at three levels (-1, 0, +1); the design uses foldover pairs plus a center run, giving orthogonal main-effect estimates that are unconfounded with two-factor interactions.

Fitted Model:

Full second-order model estimable from a DSD

= intercept

= linear main-effect coefficient

βii

= quadratic coefficient

βij

= two-factor interaction coefficient

All main effects and quadratic effects are orthogonal to each other and to two-factor interactions; a subset of interactions can be estimated once the active-effect model is identified via model selection.

Reading the Definitive Screening Design Design Layout

Results Interpretation & Model Building

Effect Hierarchy:

Primary Effects:

• • Main effects (linear terms)
• • Quadratic effects (curvature)
• • Clear effect estimates
• • Unconfounded with interactions

Interaction Selection:

• • Model-dependent estimation
• • Stepwise selection recommended
• • Cross-validation for model choice
• • Subject matter expertise crucial

Model Development:

• Full Second-Order: Y = β₀ + Σβᵢxᵢ + Σβᵢᵢxᵢ² + ΣΣβᵢⱼxᵢxⱼ

• Effect Screening: Use significance tests and effect plots

• Model Selection: AIC, BIC, or cross-validation criteria

• Validation: Residual analysis and confirmation runs

Next Steps:

• Optimization: Response surface methods if curvature present

• Confirmation: Validate optimal conditions

• Robustness: Test around optimal region

• Implementation: Scale-up considerations

Implementation Steps & Analysis

Design Construction:

1. Level Selection:

• Low (-1): Minimum practical level

• Center (0): Current/nominal operating point

• High (+1): Maximum practical level

2. Run Matrix:

• Algorithmic construction (not manual)

• Each factor appears once at each level

• No factor is at middle level in first/last run

3. Analysis Strategy:

• Fit main effects and quadratics first

• Use stepwise selection for interactions

• Validate model with diagnostics

Platform Implementation:

The sixsigmacenter.com platform automatically generates optimal definitive screening designs, performs advanced model selection for interactions, provides comprehensive effect analysis, and creates response surface models when appropriate.

When to Use Definitive Screening Designs

Ideal Applications:

Advanced Screening:

• • When curvature is suspected
• • Factors may have non-linear effects
• • Some interactions expected
• • Bridge to optimization studies

Process Characterization:

• • Complex manufacturing processes
• • Chemical/biological systems
• • Quality improvement projects
• • Robust parameter design

Factor Guidelines:

• 3-6 factors: Highly efficient (7-13 runs)

• 7-12 factors: Good efficiency (15-25 runs)

• 13+ factors: Consider in phases or other designs

• Continuous factors preferred for three-level implementation

Example Data Layout for Definitive Screening (5 factors)

11-run DSD for 5 factors with center point. Three levels per factor: -1 (low), 0 (center), +1 (high). Sample Size Recommendation: 2k+1 runs for k factors, with optional center point replication.

This is how your spreadsheet or CSV file should be structured before you upload it. Match the column names, keep one row per observation, and leave the analysis to the platform.