Ferghana Polytechnical Institute

ABSTRACT Reliability assessment of complex engineering systems is crucial for ensuring safety, performance, and cost‐effectiveness. Traditional reliability models frequently treat failure rates as static and analyze component failure rates in isolation. When dependencies are acknowledged, they are typically considered in a linear manner. This approach, however, fails to adequately capture the dynamic and nonlinear interactions that characterize real‐world systems. This paper proposes a novel reliability modeling framework that integrates dynamic failure rates and nonlinear dependencies to enhance predictive accuracy in reliability analysis. The model considers time‐varying operational and environmental factors that influence failure behavior, along with nonlinear interdependencies among system components, which can amplify risks in unpredictable ways. The proposed framework improves reliability estimation under evolving conditions. To illustrate the implications of the proposed model assumptions, the model is applied on two numerical examples and to demonstrate the impact of the model assumptions, the reliability is compared with the case where these assumptions are not considered. The findings of this research contribute to the advancement of reliability engineering by providing a more comprehensive approach to modeling failures in dynamic, interconnected systems.

In this article, the author places special emphasis on the importance of using educational technologies in working with parents to maintain and develop parental relationships with preschool-aged children. These technologies instill confidence in children, broaden their horizons, and enable them to cope with internal experiences and improve relationships with their parents.

The article discusses the use of Voltaire functional series for the analytical synthesis of optimal regulators of systems with nonlinear polynomial dynamics. The relevance of developing control methods for objects with high degrees of nonlinearity, especially in the context of symmetric polynomial systems, is indicated. The paper proposes an approach based on an approximate analytical solution of the equations of free motion using Voltaire functional series, which makes it possible to obtain accurate approximations of solutions and simplify the design of control actions. Models with symmetric and non-symmetric characteristics are considered, as well as the transformation of the initial equations into forms convenient for synthesis. The main task is to develop a method for constructing controls that ensure asymptotic stability and minimize the functionality of generalized work. The work is relevant for the automatic control of complex nonlinear systems, where classical methods are not effective enough.