For some ambiguous scenes perceptual conflict arises between integration and segregation. Initially, all stimulus features seem integrated. Then abruptly, perhaps after a few seconds, a segregated percept emerges. For example, segregation of acoustic features into streams may require several seconds. In behavioral experiments, when a subject's reports of stream segregation are averaged over repeated trials, one obtains a buildup function, a smooth time course for segregation probability. The buildup function has been said to reflect an underlying mechanism of evidence accumulation or adaptation. During long duration stimuli perception may alternate between integration and segregation. We present a statistical model based on an alternating renewal process (ARP) that generates buildup functions without an accumulative process. In our model, perception alternates during a trial between different groupings, as in perceptual bistability, with random and independent dominance durations sampled from different percept-specific probability distributions. Using this theory, we describe the short-term dynamics of buildup observed on short trials in terms of the long-term statistics of percept durations for the two alternating perceptual organizations. Our statistical-dynamics model describes well the buildup functions and alternations in simulations of pseudo-mechanistic neuronal network models with percept-selective populations competing through mutual inhibition. Even though the competition model can show history dependence through slow adaptation, our statistical switching model, that neglects history, predicts well the buildup function. We propose that accumulation is not a necessary feature to produce buildup. Generally, if alternations between two states exhibit independent durations with stationary statistics then the associated buildup function can be described by the statistical dynamics of an ARP.