An integrated statistical and machine-learning framework for FDM process optimization of PETG/0.5 wt.% graphene composites

Data-driven optimization of fused deposition modeling (FDM) parameters is often reported from small response-surface datasets, with accuracy computed on the fitting data and without examination of the experimental sequence. The novelty of this study lies in a diagnostic-first framework in which lack-of-fit testing, run-order regression, analysis of covariance, nested leave-one-design-point-out cross-validation, and optimization restricted to the convex hull of the experimental design are all completed before any process recommendation is made. A four-factor, three-level Box–Behnken design of 27 runs was used to study nozzle temperature, layer height, print speed, and raster angle for Polyethylene Terephthalate Glycol (PETG) containing 0.5 wt.% graphene. Tensile strength ranged from 19.32 to 45.50 MPa and flexural strength from 30.14 to 60.92 MPa. The quadratic raster-angle term accounted for 22.8% of the tensile variance ( P = .0023) and remained significant after adjustment for run order ( P = .0011); mean tensile strength at 90° was 25.4% higher than at 45°. Flexural strength declined by 0.602 MPa per run ( P = .0009), and the apparent temperature curvature, which carried 48.9% of the flexural variance, could not be separated from this drift. Nested cross-validated R 2 did not exceed 0.077 for tensile strength and 0.452 for flexural strength, against training values of up to 0.994. Hull-constrained desirability analysis returned 250 °C, 0.16 mm, 45 mm s −1 and 90° as a model-derived candidate with wide prediction intervals, whereas the highest strengths were observed at 270 °C under otherwise identical settings. Sequence diagnostics and held-out validation therefore determine which process conclusions can be relied upon, and the model output is presented as a candidate for confirmation rather than as a validated optimum.