Using the Monte-Carlo Method with Subsequent Approximation in Statistical-Mechanical Modeling for Estimating the Reliability of NPP Pipelines and Pressure Vessels

Abstract

For a large number of safety-critical components at existing and newly designed NPPs, the task of confirming their reliability by conventional statistical methods does not seem to be possible in view of both short periods of time for which these components have been in operation and almost no failures that have occurred for this period of time, as well as lack of analogs from the worldwide practices. One of approaches to assessing the failure probabilities of highly reliable reactor plant equipment involves application of the statistical-mechanical modeling method. For solving statistical-mechanical models, the Monte Carlo (MC) method, which has a number of advantages over analytical ones, is commonly used. However, the need to perform an excessively large number of statistical simulations in substantiating low event probabilities prompts specialists to search for alternative calculation methods. One of these techniques, proposed in this article, is a two-stage method that combines the Monte Carlo method and approximation of statistical data – the Monte Carlo method with subsequent approximation. Matters of reliability assessment with using statistical-mechanical modeling of components’ limit states are considered. The use of the proposed Monte Carlo method with subsequent approximation makes it possible to reduce the number of statistical simulations while preserving the accuracy of the results. This statement has been confirmed by a number of examples of calculating the probabilities of leaks and ductile-brittle fracture of reactor plant components.