Background:
Acceptable noise level (ANL) is a metric developed for quantifying the maximum amount of background noise one is willing and able to accept – when not tired or tensed – while involved in mundane work. ANLs have been shown to vary with the individual although they are generally independent of age, gender, and hearing sensitivity. This study develops a psychophysically based mathematical model of ANL that includes an individual’s sound judgment bias and discriminability.

Material and methods:
This paper expands Stevens’ mathematical model of sound power to develop an explicit psychophysical model. The model includes an individual’s judgment bias and sound discriminability to predict their ANL and uncovers the reason for individual ANL variability.

Results:
Using simulated data, the developed model shows how an individual’s ANL can be predicted based on their sound discriminability and judgment bias score. A regression analysis on the simulated data showed an R-square of 0.85 (p = 0.0001) between discriminability and simulated ANL data. There was a logarithmic relationship between individual ANL and sound discriminability.

Conclusions:
The model well replicates human auditory sound processing. The higher the ANL, the higher the individual’s judgment bias toward the background noise and the better their ability to discriminate between the signal and background noise.