The tutorial covers modern problems related to the reliability of machines and complex systems, including equipment for machine-building industries, automatic lines, GPS, etc. Mathematical methods for quality and reliability management of products are given. The basic concepts of quality of products and their reliability during their operation, the basics of probability theory and mathematical statistics for technical applications are considered. Methods for statistical evaluation and verification of quantitative estimates are outlined, as well as verification of estimates for qualitative features, the use of variance and correlation analysis with a small amount of data.