Methods to optimize rare-event Monte Carlo reliability simulations for Large Hadron Collider Protection Systems

Machine Protection Systems of the Large Hadron Collider (LHC) are safety-critical systems that adhere to stringent reliability and availability requirements. High reliability is required because the energy of the particles beam and the energy stored in the magnets are high enough to damage the machine beyond repair. High availability is required to maximize the amount of data collected by the experiments. Both constraints will become even more critical for LHC upgrades (High Luminosity LHC) and a possible larger accelerator (Future Circular Collider). The field of availability and reliability studies provides a variety of tools well-suited for those purposes. Among them, Monte Carlo simulation is a remarkably flexible and versatile option for in-depth analyses of complex systems. This thesis reviews available methods for increasing computations efficiency in generic rare-event simulations framework used for reliability engineering purposes. Efforts to reduce the workload of MC simulations have been ongoing for a very long time, since the 1950s, and include methods such as importance sampling (IS), importance splitting (ISp), and randomized quasi-Monte Carlo (RQMC) method. More recent developments usually build on top of those methods. Based on a review of popular methods employed across the rare-event simulations field, ISp and RQMC methods were selected as promising solutions for our reliability and availability simulations. The empirical tests are a working proof of concept and show potential for remarkable improvements for reliability simulations of rare events with ISp and availability prediction with RQMC. Alongside the rare-event methods, the project also involved an analysis of HL-LHC Energy Extraction system reliability, which serves as an introduction for reliability modelling and is presented in a report attached to the thesis. The project involved contributions to the AvailSim4 MC framework developed at CERN.