The standard approach for detecting mooring line failures for position moored vessels is by measuring the tension in the mooring lines, either directly or indirectly. The sensors measuring the line tensions are often hard to maintain due to being mounted under water, and determining if a loss of tension is a line failure or a sensor failure can be difficult. This thesis investigates a different approach, using statistical analysis of only the position of the vessel to detect mooring line failures. This is achieved by creating a mathematical model of the vessel motion for each of the possible failure scenarios, in addition to the no failure scenario. For each scenario a passive observer is implemented based on the appropriate mathematical model. The observers estimate the states of the vessel. The quality of the estimated states will depend on how the actual behaviour of the vessel compares to what is predicted by the model assuming a certain failure scenario. Two different methods are used to analyse these estimates to determine which scenario is believed to be correct: dynamic hypothesis testing (DHT) and maximum likelihood estimation (MLE). In short, DHT calculates the probability of each scenario being true, and MLE calculates the likelihood of each scenario. In simulations both methods show promising results in their ability to detect mooring line failures. Failures are detected within a couple of minutes, when subjected to both wave and current disturbances. However, an implementation error in the simulator used causes the results to not be directly transferable to a real world scenario.