Psychoacoustic experiments indicate that the human auditory system is less sensitive than predicted by classical signal detection theory on a simultaneous masking task [C. M. Reed et al., J. Acoust. Soc. Am. 53, 1039--1044 (1973)]. Traditionally, the difference between the matched filter and the experimental performance has been compensated for by assuming an additional internal additive noise. However, this noise has not been completely explained in physiological terms. The inconsistency may also partially be the result of the suboptimal application of signal detection theory. To investigate this discrepancy, signal detection theory is integrated with Patterson's model of the human auditory system [R. D. Patterson et al., J. Acoust. Soc. Am. 98, 1890--1895 (1995)]. The performance of the optimal detector for a simultaneous masking task is compared to experimental data, allowing the theoretical performance bounds to be determined and the model to be verified. The results of this work suggest that with a more appropriate application of signal detection theory it is possible to partially explain the difference in performance between the matched filter and experimental data as the result of physical processes inherent in the auditory system. Utilizing a priori information regarding these processes results in an approach which more accurately predicts psychophysical behavior.