Sensitivity Analysis-Integrated Full Factorial Design
Also known as: SA-FFD, full factorial design with sensitivity analysis, factorial-based sensitivity analysis, FFD-SA
Sensitivity analysis-integrated full factorial design combines exhaustive factorial experimentation — where every combination of factor levels is tested — with systematic sensitivity analysis to quantify how much each input factor drives variation in the output response. This hybrid approach provides both reliable effect estimates and a ranked picture of factor importance, guiding engineers and scientists toward the levers that truly matter for system performance.
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When to use it
Use this method when you need to understand both how factors affect a response and which factors matter most — especially in engineering design, process optimization, and computational model validation where all factors can be physically or computationally set to predetermined levels. It is most valuable when the number of factors is modest (typically k ≤ 7 for two-level designs, keeping run counts manageable) and when interaction effects are suspected. Do NOT use it when the number of factors is large (k > 7 at two levels yields 128+ runs, making full factorial infeasible — prefer fractional factorial or Plackett-Burman screening instead). Also avoid this approach when factor levels cannot be precisely controlled, when runs are prohibitively expensive, or when only a rough ranking of factor importance is needed (Morris one-at-a-time screening is then more efficient).
Strengths & limitations
- Complete resolution of all main effects and interactions — no aliasing — enabling unambiguous effect estimation.
- Sensitivity indices provide a quantified, variance-decomposed ranking of factor importance beyond simple significance flags.
- Detecting interaction effects is straightforward, which is critical for systems where factors do not act independently.
- Results are directly usable for subsequent response surface modeling or optimization because the full factorial design supports higher-order fitting.
- Transparent and easy to communicate to engineering and management audiences unfamiliar with advanced DOE methods.
- Run count grows exponentially with the number of factors (2^k), making the method impractical for more than 6–7 factors at two levels without resources for many experiments.
- Sensitivity indices derived from a fitted factorial model inherit any model misspecification; nonlinear or non-monotonic factor effects may not be fully captured by a linear factorial model.
- Variance-based sensitivity analysis assumes sufficient output variance exists to decompose; near-deterministic outputs or very small experimental error can make index estimation unstable.
- The design space must be pre-specified; sensitivity rankings apply only within the tested factor ranges and may shift if boundaries change.
Frequently asked
How is this different from a standard full factorial design?
A standard full factorial design estimates effects and tests their statistical significance. The sensitivity-analysis-integrated variant adds a second analytical layer that decomposes the total output variance and quantifies each factor's proportional contribution — yielding a ranked importance measure (sensitivity index) that goes beyond a binary significant/non-significant verdict. This is especially useful when multiple factors are significant and you need to prioritize which ones to control most tightly.
Which sensitivity index should I use — first-order or total-order Sobol indices?
First-order Sobol indices (S_i) measure a factor's direct contribution to output variance, ignoring interactions. Total-order indices (S_Ti) include all interaction contributions involving that factor. If S_Ti is substantially larger than S_i, the factor is important primarily through interactions. Always report both when interactions are present. If the sum of all S_i is close to 1, interactions are negligible and first-order indices suffice.
Can I use this method with simulation models rather than physical experiments?
Yes — in fact, variance-based sensitivity analysis integrated with factorial designs is particularly common in computational simulation studies, where run cost is fixed and all factor combinations can be evaluated exactly. The same design and analysis workflow applies; the only difference is that runs are computer evaluations rather than physical experiments.
What if my response is non-normally distributed?
Variance-based sensitivity indices are distribution-free — they decompose variance regardless of the output distribution shape. The ANOVA component of the factorial analysis assumes normally distributed residuals; if this assumption is violated, apply a transformation (log, Box-Cox) or use a generalized linear model before estimating effects.
When should I prefer fractional factorial design over full factorial for sensitivity analysis?
When the number of factors exceeds 6–7, a full factorial design becomes prohibitively expensive. Fractional factorial designs with Plackett-Burman arrays or Resolution IV/V fractions provide sensitivity screening at far fewer runs. The trade-off is partial confounding of higher-order interactions, which limits the precision of sensitivity index estimation. A common strategy is to screen with a fractional design, then follow up with a full factorial on the small subset of important factors identified.
Sources
- Saltelli, A., Ratto, M., Andres, T., Campolongo, F., Cariboni, J., Gatelli, D., Saisana, M., & Tarantola, S. (2008). Global Sensitivity Analysis: The Primer. John Wiley & Sons. ISBN: 978-0470059975
- Montgomery, D. C. (2017). Design and Analysis of Experiments (9th ed.). John Wiley & Sons. ISBN: 978-1119113478
How to cite this page
ScholarGate. (2026, June 3). Sensitivity Analysis-Integrated Full Factorial Design. ScholarGate. https://scholargate.app/en/experimental-design/sensitivity-analysis-integrated-full-factorial-design
Which method?
Set this method beside its closest kin and read them side by side — the library lays the books on the table; the choice is yours.
- Design of experimentsExperimental design↔ compare
- Response Surface MethodologyExperimental design↔ compare
- Sensitivity analysis-integrated response surface methodologyExperimental design↔ compare