The results of the research published in the article will be useful for logistic support specialists who are involved in the organization of the operation and renewal of weapons and military equipment. The article discusses the methodical approach to solving the question of ensuring the choice of a rational option for maintaining the efficiency of the anti-aircraft missile system, taking into account the impact of moral aging of the third kind. The publications in the scientific and technical literature on the issues of predicting the durability of weapons and military equipment based on logical-probabilistic models, which take into account both changes in the properties of components of anti-aircraft missile systems, as well as the possibility of its logistics support system, analyzed the task of choosing a rational option for maintaining the technical condition of anti-aircraft missile systems, taking into account the above factors, they were not considered, which allowed to determine the unsolved scientific problem, which consists in the further development of the scientific and methodological approach of choosing a rational variant of maintaining the technical condition of the anti-aircraft missile systems, taking into account the change of the properties of the elements of the equipment and the capabilities of the logistics system to restore its technical resource.
A mathematical model of choosing a rational option for maintaining the technical condition of an anti-aircraft missile system is described taking into account changes in the properties of equipment elements and the capabilities of a system for restoring its technical resource. It is shown that the choice of one or another variant of maintaining the operability of an anti-aircraft missile system should be based on assessments of the technical and economic efficiency of compensating for the degradation of resource fail-safety. It is shown that to compensate for the degradation of resource fail-safety of the air defense system's operability, methods of modernizing electronic equipment and methods to increase the availability of operational processes can be used. Based on the mathematical apparatus of the trees of the limiting state, analytical expressions are obtained for calculating the estimates of the indicators of technical and economic efficiency of the application of various methods of compensating for resource fail-safety. An approach is proposed to justify the choice of the most rational option for maintaining the health of air defense systems by the criterion of maximum technical and economic efficiency based on the results of ranking estimates of technical and economic efficiency indicators.