Sensitivity Analysis-Integrated Response Surface Methodology
Also known as: SA-RSM, RSM with sensitivity analysis, sensitivity-augmented RSM, response surface methodology with factor screening
Sensitivity analysis-integrated RSM couples a structured experimental design with a formal sensitivity analysis of the fitted response surface model. After estimating a polynomial surrogate from designed experiments, global or local sensitivity indices are computed to quantify each input factor's relative contribution to output variability. This allows practitioners to identify which factors truly drive the response before committing to full optimization, reducing cost and improving the reliability of the final optimum.
Read the full method
Sign in with a free account to read this section.
Method map
The neighbourhood of related methods — select a node to explore.
When to use it
Use SA-RSM when you have a moderate-to-large number of continuous input factors (typically 3–10) and need to both identify the key drivers of a response and locate the optimum in one integrated workflow. It is especially valuable in chemical engineering, materials processing, and product formulation where experimentation is expensive and some factors may be practically irrelevant. The method requires continuous quantitative response data and at least a fitted second-order model; it is not suitable for purely categorical designs, very sparse data, or situations where the true response is discontinuous or highly non-smooth. Avoid it when the number of runs required for an RSM design is already prohibitive — in that case a space-filling design with surrogate-based SA may be preferable.
Strengths & limitations
- Identifies which factors truly drive the response, enabling targeted process control and factor fixation.
- Combines screening and optimization into a single model-based workflow, reducing the need for additional confirmatory experiments.
- Global sensitivity indices (Sobol) provide variance-decomposition insight that local RSM optima alone cannot supply.
- Improves robustness of the optimum by highlighting interactions that must be controlled tightly.
- Applicable across engineering, chemistry, pharmaceuticals, and environmental science.
- Requires a valid second-order surrogate; if the true response is highly nonlinear or discontinuous the polynomial fit may mislead both RSM and SA.
- Global SA (Sobol indices) can be computationally intensive even on a surrogate model when the factor space is large.
- Sensitivity results depend on the assumed input factor distributions; wrong distributional assumptions yield misleading indices.
- Does not replace physical validation — the predicted optimum from the surrogate must be confirmed with at least one confirmation run.
Frequently asked
What is the difference between SA-RSM and just running RSM with ANOVA?
ANOVA within RSM identifies statistically significant terms in the polynomial model, which is a local-model-based test of whether a coefficient differs from zero. Sensitivity analysis — particularly Sobol indices — apportions the total variance of the response across factors and their interactions globally over the input space. SA gives a magnitude-of-influence ranking that ANOVA p-values do not directly provide, and is not affected by arbitrary significance thresholds.
Do I need extra experimental runs to perform the sensitivity analysis?
No. Sensitivity analysis is performed on the already-fitted response surface model (the surrogate), not on additional physical experiments. The SA propagates uncertainty through the polynomial equation analytically or via Monte Carlo sampling from the surrogate, so the experimental cost is the same as standard RSM.
Which sensitivity method should I use — Morris screening or Sobol indices?
Morris elementary effects screening is computationally lighter and excellent for initial ranking of many factors. Sobol variance-decomposition indices are more precise and capture interaction contributions explicitly, but require more model evaluations. For a polynomial RSM surrogate, Sobol indices are cheap to compute because model evaluation is fast, so they are generally preferred when you need quantitative variance attribution.
Can SA-RSM be applied when I have multiple responses?
Yes. Each response gets its own fitted model and its own set of sensitivity indices. Factors that are influential for all responses become primary control targets; factors influential for only one response allow targeted control strategies. Desirability-function optimization is then applied to the set of simplified models simultaneously.
Is SA-RSM the same as robust RSM?
They are related but distinct. Robust RSM explicitly models noise factors as inputs and seeks an optimum that is insensitive to their variation. SA-RSM computes sensitivity indices over the full factor space to identify which factors matter most, but does not necessarily distinguish control from noise factors. The two approaches can be combined: run a robust RSM design, then apply SA to the fitted mean and variance models separately.
Sources
- Myers, R. H., Montgomery, D. C., & Anderson-Cook, C. M. (2016). Response Surface Methodology: Process and Product Optimization Using Designed Experiments (4th ed.). Wiley. ISBN: 978-1118916018
- Saltelli, A., Ratto, M., Andres, T., Campolongo, F., Cariboni, J., Gatelli, D., Saisana, M., & Tarantola, S. (2008). Global Sensitivity Analysis: The Primer. Wiley. ISBN: 978-0470059975
How to cite this page
ScholarGate. (2026, June 3). Sensitivity Analysis-Integrated Response Surface Methodology. ScholarGate. https://scholargate.app/en/experimental-design/sensitivity-analysis-integrated-response-surface-methodology
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.
- Box-Behnken DesignExperimental design↔ compare
- Central Composite DesignExperimental design↔ compare
- Design of experimentsExperimental design↔ compare
- Optimization-assisted response surface methodologyExperimental design↔ compare
- Response Surface MethodologyExperimental design↔ compare