Probability and Information Entropy in the Analysis of Reliability of Technical Systems

The paper outlines the issues of reliability analysis of complex technical systems. The justification of the need to perform reliability analysis of complex technical systems, the structure of which is a network, is given. We propose to apply for this purpose, in addition to probabilistic characteristics, information entropy calculated based on the K. Shannon model. A classical assessment of a random event in reliability analysis as a possible outcome (test result) is given. Following the theories of probability and information, the classical measures of probability and their relationship to the measure of uncertainty of information (entropy) are considered. The role of the private entropy obtained as a result of the tests and its participation in the classical Shannon model are indicated. A distinctive feature of this model is the differentiation of entropy into components related to two incompatible events with the probability of failure-free operation and the probability of failure. This avoids mixing entropies in the additive event accounting process. According to the classical theorems of addition and multiplication of probabilities, as well as consideration of compatible, incompatible and overlapping events, mathematical expressions of entropy are presented. They allow us to assess the level of information uncertainty in the task of reliability analysis for subsequent comparison and selection of system structures.