Risk assessment is an integral part of an enterprise's quality management system. The risk of low quality products is the most significant risk, as it is directly related to the concept of enterprise competitiveness. The paper analyzes the scientific papers related to the assessment of the quality of products, processes and services, their disadvantages, possible limits of application. It is proposed to use mathematical dependences to obtain estimates of product quality indicators on a dimensionless scale. Knowing the density function of random variables of product quality indicators and knowing the mathematical dependence of their estimates on a dimensionless scale, it is proposed to obtain the density function of estimates. Knowing the function of the density of estimates of quality indicators, it is proposed to find the probabilities of risks of the assessment of quality indicators in any given interval on a dimensionless scale. A method for assessing the risks of low quality products has been developed