The application of noise to a nonlinear system can have the effect of increasing the signal transmission of the system through the phenomenon of stochastic resonance (SR). This paper presents an analytical characterization of the dependence of the signal transmission performance of an organic field-effect transistor (OFET) on external noise. Similarly to the threshold of a nonlinear system, the additive internal noise of the system can be used to control the emergence of SR. Internal noise or the addition of random numbers to the system enables one to observe the SR phenomenon in an OFET under an intrinsically nonresonant condition. Internal noise plays a thresholdlike role, but it functions in a different manner. The fluctuations in performance due to external noise become smaller when the effect of internal noise becomes dominant compared with that of the threshold. In conclusion, it is found that internal noise plays a robust thresholdlike role with respect to variations in external noise intensity.