Roll drafting is an important unit operation that transforms fiber bundles into attenuated ones, improving their properties with more efficient material usage. Fibers are thus thrown into a flow field having constraints at both ends incurring layer-to-layer flow shearing, which governs the individual fiber movement. The parameters of the flow characteristics are disturbed or changed during processing and the output of the roll drafting operation can have either more or less fluctuating properties. In this research, we perturbed the model parameters related to the roll drafting process to identify their effects on the process dynamics and consequently the quality of the processed product. Based on the random phase spectral method, stochastic signals having an exponentially decaying auto- correlation function were generated and applied to the mathematical model that described the dynamic behavior of the flowing bundle. Thus, the profiles of the linear density and velocity of the bundle flow field in steady state were simulated. In extreme perturbations the bundle can break, which was simulated and confirmed by experiments. This research showed that a singular point in the draft zone existed which implied a bundle breakage. The singular point in the draft zone could be attributed to the inadequate set-up of the process conditions, specifically, to two parameters in the model: one was related to the bundle properties and the other to the process conditions. Considering the bundle property related parameter as a stochastic process, the range of the parameter variation to ensure a continuous drafting operation was limited. The influence of the perturbations on the draft process also became more sensitive as the process speed and the draft ratio increased.