Adding noise to sensory signals generally decreases human performance. However, noise can improve performance too, through a process called stochastic resonance (SR). This paradoxical effect may be exploited in psychophysical experiments to provide insights into how the sensory system processes noise. Here, I develop an extension on signal detection theory to model stochastic resonance. I show that the inclusion of lapse rate allows for the occurrence of stochastic resonance in terms of the performance metric d', when the criterion is set suboptimally. High levels of lapse rate, however, cause stochastic resonance to disappear. It is also shown that noise generated in the brain (i.e., internal noise) may obscure any effect of stochastic resonance in experimental settings. I further relate the model to a standard equivalent noise model, the linear amplifier model, and show that lapse rate scales the threshold versus noise (TvN) curve, similar to the efficiency parameter in equivalent noise (EN) models. Therefore, lapse rate provides a psychophysical explanation for reduced efficiency in EN paradigms. Furthermore, I note that ignoring lapse rate may lead to an overestimation of internal noise in EN paradigms. Overall, describing stochastic resonance in terms of signal detection theory, with the inclusion of lapse rate, may provide valuable new insights into how human performance depends on internal and external noise. It may have applications in improving human performance in situations where the criterion is set suboptimally, and it may provide additional insight into internal noise hypotheses related to autism spectrum disorder.