This article proposes a game-based decision support model for determining the optimal time to start modernizing a weapon and military equipment (WMH) system. In the context of one-sided tracking games, where the military analyzes the pure strategy of the opponent, the authors consider a situation where the military has to determine the best time to start modernizing the weapons and military equipment. One of the key aspects of determining the optimal time to start modernization is to analyze the enemy's strategy. The article provides recommendations for choosing the moment to start analyzing the enemy's pure strategy in games with one-sided tracking. Within this game model, the military can consider different enemy strategies and their impact on the outcome of the conflict. In particular, decisions on modernization of weapons and their impact on combat performance are taken into account. The use of a decision support game model to determine when to start modernizing a WME system can be useful for military strategists and analysts involved in planning and managing military operations. It helps to understand how to take into account the actions of adversaries and maintain the competitiveness of military forces through timely and optimal modernization of weapons and military equipment. Taking into account game aspects and the use of mathematical models can improve strategic planning and decision-making in the context of modernization of weapons and military equipment. The application of a game model can help determine the optimal time to start modernization, which contributes to achieving strategic goals and ensuring military superiority. It can also help to use resources efficiently and reduce the risks associated with the obsolescence of military equipment. In the future, the game model can be further improved by adding new factors and refining mathematical algorithms. Keywords: model, modernization, weapons and military equipment system, strategy, game theory.

The article poses a scientific problem, which is solved by using electromechanical mechanisms with an automatic control scheme and tracking the tension of the caterpillar within the required limits. The analysis of scientific papers revealed a number of disadvantages that are inherent in tracked propellers with existing track tensioning mechanisms: a significant drop in the efficiency at high speeds of a track with a rubber-metal hinge due to high stretching coefficients, which leads to a decrease in the coefficient of adhesion of the track; significant deterioration in maneuverability due to the possibility of the decrease of the track from the idler wheel under certain conditions; the inability to change the tension of the tracks when turning the machine, the inability to automatically respond to a change in the type of soil. Summing up the results of the literature review on the topic, we can single out a part of the previously unsolved problem, namely: the problem of matching the track tension to the external and internal operating conditions of the tracked mover is multifactorial, and its solution is a complex technical problem. Such mechanisms use widely adjustable DC motors with built-in electromagnetic brakes. It is obvious that the installation of these electric motors will provide the necessary speed, automatic or in accordance with the signals of the human operator, the necessary regulation of the tension of the tracks. which will significantly increase the controllability of the tracked vehicle at high speeds, significantly increase the patency of the tracked vehicle, obtain a positive effect on the dynamic performance of the tracked vehicle, achieve the maximum increase in the maximum speed, increase the efficiency of the tracked propeller up to 10% depending on the driving conditions by reducing the caterpillar bypass, reduce fuel consumption by up to 6% by increasing the efficiency of the caterpillar mover, increase the durability of the tracks. Keywords: combat vehicles, tracked chassis, weapons and military equipment repair.

One of the main tasks of the state policy in the field of defense is to maintain the Armed Forces in a combat-ready state, other military formations formed in accordance with the laws, law enforcement agencies of special purpose in the security and defense sector, the main role is given to equipping them with the latest types of weapons and military equipment to ensure protection of state sovereignty and territorial integrity of the state. In the conditions of the current state, the specified equipment with new models of domestic production is not so fast, and the supply of weapons and military equipment from Western partners requires the training of specialists, therefore, taking into account the current state of the domestic fleet of weapons and military equipment, it is urgent to search for alternative methods for maintaining weapons and military equipment in working condition. The article describes the method of formalizing the process of searching for failures of the weapons and military equipment (WEQ) system and describes the algorithm for finding the optimal sequence of its control in order to find faulty devices. The article uses the theory of mathematical models of optimal decision-making in conflict conditions – game theory. According to the research results, it was found that the proposed method of formalization of the failure process of the weapons and military equipment system and the given algorithm for finding the optimal sequence of its control can be implemented with the development of automatic systems of control and diagnostics of weapons and military equipment systems. Keywords: failure, weapon system and military equipment, state, strategy, game theory.