MATHEMATICAL MODELING OF SAFETY CONTROL PROCESSES AT NUCLEAR POWER PLANTS

This paper examines the use of mathematical modeling to enhance the safety of nuclear power plants (NPPs). The study demonstrates that reaction time plays a crucial role in accident prevention: if an operator takes action within 30 seconds, the probability of preventing an accident is 95%, whereas a 5-minute delay reduces this probability to 30%. The impact of preventive maintenance and system redundancy on reliability is also analyzed. Without maintenance, the probability of equipment failure after 1000 hours of operation reaches 40%, whereas regular inspections reduce this to 15%, and redundancy further lowers it to 8%. Additionally, cascading failures were studied, showing that as the number of interdependent components increases from 3 to 10, the risk of total system failure rises from 15% to 80%. The paper provides practical recommendations for improving NPP reliability, including the automation of monitoring, the implementation of predictive algorithms, and the use of machine learning for failure forecasting.