This paper proposes a fractional fuzzy extension of the logistic growth equation (LGE) for modelling nonlinear growth processes characterised by memory effects and uncertainty in model parameters. Triangular fuzzy numbers (TFNs) represent the intrinsic growth rate and carrying capacity, while the Caputo fractional derivative replaces the first-order derivative to account for memory-dependent dynamics. To obtain an analytical solution, the classical residual power series method (RPSM) is systematically extended to the resulting fuzzy fractional model using residual conditions and the α -cut representation of fuzzy quantities. The proposed formulation generates the series coefficients recursively without linearization or time discretization and provides explicit lower and upper solution bounds. A manufacturing-process application is presented in which the evolution of non-conforming items is modeled under uncertain operating conditions and fractional memory effects. The results demonstrate the convergence of the proposed truncated series solution and show that the fractional order significantly influences the predicted defect evolution, while fuzzy parameters provide a bounded representation of operational uncertainty. The proposed approach therefore provides an analytical framework for incorporating memory effects and parameter uncertainty into logistic-type models, with potential applications in industrial process monitoring and preventive maintenance planning.