The paper describes the distribution of polyacrylonitrile roving filaments lengths in terms of risk theory by the normal distribution law. We identify the optimal fiber length experimentally. However, it depends on the type of fibrous material, its optimal dosage as a percentage by weight of asphalt concrete mixture, and fiber density. Also research dwells on the statistical methods of identifying the standard deviation of the cut length of fibre filaments on special cutting equipment which provides the substantiation of the law of distribution of fibre filament lengths. The results ensure the risk assessments and reliability of reinforcement of asphalt concrete mixture with polyacrylonitrile fiber. Moreover, according to the research, density of polyacrylonitrile fiber filaments affects the spread of the distribution law of the lengths of the filaments as follows: the higher the density, the lower the standard deviation of the cut fibre lengths; the denser the polyacrylonitrile fibre filaments, the lower the variability of the cut filament lengths.