The present review deals with the issues of ensuring and maintaining high reliability during the entire life cycle of a technical system in the engineering sector, i.e., determining the requirements, design, research, development, production, installation, operation, and disposal of the product. Owing to their reliability, special attention is given to the technical systems in companies for several reasons. These mainly include the need to achieve reliability and safety by using the product, but also in terms of economic, social, and ecological aspects. We understand reliability as a primary feature, and during the design of new products, it is necessary to predict its course and characteristics appropriately. Reliability needs to be analyzed with the help of partial reliability properties throughout the entire life cycle of the product. To achieve the required level of reliability, we use reliability analyses, which are successfully implemented to examine and predict reliability indicators. The present review provides a comprehensive overview of reliability analysis and offers a mathematical basis for individual sub-indicators. In the article, the analysis of system reliability is described as a process, the essence of which is the acquisition, examination, and organization of specific information. This information is significant for the given system and necessary for making decisions according to the specified goals, which ensure an objective assessment of the overall level of reliability.