The precedence effect describes our ability to perceive the spatial characteristics of lead and lag sound signals. When the time delay between the lead and lag is sufficiently small we will cease to hear two distinct sounds, instead perceiving the lead and lag as a single fused sound with its own spatial characteristics. Historically, precedence effect models have had difficulty differentiating between lead/lag signals and their fusions. The likelihood of fusion occurring is increased when the signal contains periodicity, such as in the case of music. In this work we present a cepstral analysis based perceptual model of the precedence effect, CEPBIMO, which is more resilient to the presence of fusions than its predecessors. To evaluate our model we employ four datasets of various signal types, each containing 10,000 synthetically generated room impulse responses. The results of the CEPBIMO model are then compared against results of the BICAM. Our results show that the CEPBIMO model is more resilient to the presence of fusions and signal periodicity than previous precedence effect models.