An innovative DMAIC and response surface methodology framework for optimizing carbon xerogel synthesis in proton exchange membrane fuel cells

Proton exchange membrane fuel cells require catalytic supports with high surface area and controllable surface chemistry to ensure catalyst dispersion, stability, and durability. This study presents an integrated framework combining Define–Measure–Analyze–Improve–Control (DMAIC), Design of Experiments, and Response Surface Methodology to optimize carbon xerogel synthesis for membrane electrode assembly supports in a public research environment. A Box–Behnken design with three factors at three levels (15 runs) evaluated (i) acid type in the sol–gel step, (ii) carbonization temperature (900–1100 °C), and (iii) carbonization time (10–30 min). Two critical-to-quality responses were measured: Raman ID/IG ratio (defect density/functionalization) and Brunauer–Emmett–Teller specific surface area. Second-order regression models showed strong statistical performance and were embedded in a weighted desirability function solved with the Generalized Reduced Gradient algorithm for multi-response optimization. Optimal conditions consistently involved sulfuric acid, temperatures around 970–1020 °C, and 30 min, jointly improving Raman ID/IG ratio and surface area. Confirmation experiments under three representative scenarios yielded values within two-sided 95% prediction intervals, demonstrating model predictability and process reproducibility. The DMAIC cycle concluded with standard operating procedures for knowledge transfer and control. Limitations include the restricted design space and the absence of electrochemical durability and stack-level validation. Even so, the framework proved effective and transferable, aligning optimization with traceability and robustness needs in fuel cell research and development.