Mathematical model of educational event reliability as a random process

Abstract

This article addresses the application of probability theory in models of education reliability, specifically focusing on the development of events over time. The use of non-monotonic models introduces random variables that exhibit non-monotonic behavior with respect to time, representing the final outcomes of the educational process under the influence of various factors. The article utilizes the Logical-probabilistic method to analyze the reliability of education systems. Mathematical parameters and solutions for educational events are defined, and a model is created to provide a scientific analysis of these events. The article presents a task model involving a system with redundancy and Poisson failure flows. The system consists of a main element and reserves, and their failure and activation processes are described. Furthermore, the article introduces a mathematical model for system reliability using logical algebra and logical reasoning. The reliability of the system is expressed as a logical function dependent on the states of its elements. The article concludes by emphasizing the importance of mathematical modeling and analysis in understanding and ensuring the reliability of educational systems.