Abstract: The previous research demonstrated that the dispersion of the accelerated points of floating fibers is the main reason of the unevenness of the drafted slivers.This paper theoretically analyzed the condition under which the fiber in the drafting zone is accelerated.The condition of the fiber acceleration is expressed in a probabilistic form regarding the condition that the drafting forces are greater than the control forces.The dynamic law of the fast and slow fibers in any profile in the drafting zone is assumed and for a fiber of given length the variance of the accelerated points is obtained.Therefore the distribution function principle can be used to give the overall variance of the accelerated points.The pressure and friction coefficients are incorporated into the variance.Further analysis can be drawn on the basis of the variance obtained.