MATHEMATICAL MODELING OF THE PROCESSES OF INCREASING THE RELIABILITY OF THE NAVIGATION COMPLEX THROUGH REDUNDANCY

The purpose of the article is research and mathematical modeling of how the reliability of the navigation complex can be increased by adding redundant elements to the system. The presented article examines some issues of determining the stability of technical systems, first of all, from the point of view of their reliability (probability of failure-free operation). A number of relevant problems related to increasing the reliability of systems by adding redundant elements are considered. The assessment of various schemes for redundancy of system elements was carried out and their mathematical modeling was carried out. For systems consisting of nonuniformly reliable elements, the validity of replacing their reliabilities with an averaged value has been investigated. It is shown that such a replacement gives somewhat inflated system reliability values, and makes sense only with a small dispersion of reliability values (probabilities of failure-free operation) of system elements. At high dispersion values, the relative error of the system reliability calculation increases sharply (>10%). An example of greater or less deep redundancy of the least reliable elements of the system is also presented, which significantly (more than twice) increases the reliability of the system as a whole. The directions of further research are defined, such as the use of the concept of full probability and Bayesian (posterior) probabilities of the relevant hypotheses. Keywords: redundancy, reliability, probability of trouble-free operation, navigation complex, modeling.