Safety is paramount to the chemical process industries. Because many processes operate at high temperatures and/or pressures, involving hazardous chemicals at high concentrations, the potential for accidents involving adverse human health and/or environmental impacts is significant. Thanks to research and operational efforts, both academically and industrially, the occurrences of such incidents are rare. However, disastrous events in the chemical manufacturing industry are still of relevant concern and garner further attention – the Deepwater Horizon incident (2010) and the Texas City refinery explosion (2005) being two recent examples. Many techniques have been developed to understand, quantify, and predict alarm and safety system failures. In practice, hazards are identified using Hazard and Operability (HAZOP) analysis, and a network of independently-acting safety systems works to maintain the probabilities of such events below a Safety Integrity Level (SIL). The network of safety systems is studied with Layer of Protection Analysis (LOPA), which uses failure probability estimates for individual subsystems to project the failures of entire safety system networks. With few alarm and safety system activations over the lifetime of a chemical process, particularly the critical last-line-of-defense systems, the failure probabilities of these systems are difficult to estimate. Statistical techniques have been developed, attempting to decrease the variances of such predictions despite few supporting data. This thesis develops methods to estimate the failure probabilities of rarely activated alarm and safety systems using process and operator models, enhanced by process, alarm, and operator data. Two repeated simulation techniques are explored involving informed prior distributions and transition path sampling. Both use dynamic process models, based upon first-principles, along with process, alarm, and operator data, to better understand and quantify the probability of alarm and safety system failures and the special-cause events leading to those failures. In the informed prior distribution technique, process and alarm data are analyzed to extract information regarding operator behavior, which is used to develop models for repeated simulation. With alarm and safety system failure probabilities estimated for specific special-cause events, near-miss alarm data are used, in real-time, to enhance the predictions. The transition path sampling method was originally developed by the molecular simulation community to understand better rare molecular events. Herein, important modifications are introduced for application to understand better how rare safety incidents evolve from rare special-cause events. This method uses random perturbations to identify likely trajectories leading to system failures – providing a basis for potential alarm and safety system design.