<p>The purpose of this manuscript is to investigate the impact of uncertain parameters on the electrical signal output performance and stability of functionally graded materials (FGMs) flexoelectric nanobeams using the quasi-Monte Carlo method. The model incorporates surface effects and the Winkler–Pasternak linear elastic foundation. Based on quasi-static theory, analytical expressions are derived for the output voltage (electrical open-circuit state), output charge (electrical short-circuit state), and effective piezoelectric coefficient (electrical short-circuit state). The analysis results indicate that the gradient index and flexoelectric coefficient substantially increase the output charge and effective piezoelectric coefficient under electrical short-circuit conditions while reducing the output voltage under electrical open-circuit conditions. Increasing the length and dielectric constant of the beam suppresses the output voltage in the electrical open-circuit state, while an increase in thickness reduces the system’s stability. Sensitivity analysis reveals that the dielectric constant has the most significant influence on the output voltage in the electrical open-circuit state, whereas the beam length exerts the most pronounced effect on the output charge and the effective piezoelectric coefficient under electrical short-circuit conditions. This study provides a theoretical foundation and practical guidance for optimizing the design of micro- and nanoenergy harvesters and sensors.</p>