The increasing demand for renewable energy sources has brought about the need for innovative solutions to harness energy from the wind. One such solution is floating offshore wind turbines (FOWT), which offer several advantages over traditional onshore wind turbines and bottom-fixed offshore wind turbines. FOWTs present a challenge concerning overall cost, using fewer mooring lines than seen previously in the offshore industry. Statistically, these mooring line failures are expected to occur annually in large turbine fields and could result in untethered turbines causing extensive financial and reputational damage. It is, therefore, critical to understand whether a single mooring line failure could endanger the entire system, creating a risk that must be reduced to a level that is as low as reasonably practicable (ALARP). The Tetraspar demo FOWT off the coast of Norway is used as a model to investigate the influence of mooring line failure on the mooring system. This thesis investigates the potential risks associated with the three-leg mooring system of a FOWT following mooring line failure. The research employs a simulation-based methodology coupled with insights from previous studies and a fault tree analysis (FTA) to estimate the increase in failure probability of a complete mooring system in case of a single mooring line failure relative to an intact system. Specific assumptions underpin this investigation, including a six-month repair time bridging winter weather till the repair campaign and categorising two mooring line failures in a three-leg mooring system as a complete system failure. This thesis's research is divided into two categories: new failure modes specific to Tetraspar and altered failure modes, which are fatigue-related modes already included in the FTA, adopted from previous studies. Findings highlight the risk of Tetraspar capsizing after a mooring line failure and potential issues with slack line events and fibre sections of the mooring line touching the seafloor. Low-frequency second-order drift significantly increases fatigue in the mooring lines and fairleads, evidenced by an over 1200\% fatigue increase in some instances. A FTA consolidates these findings, showing a total failure probability increase in broken line state of between 32\% to 137\% based on the assumptions made. The study reveals a notable increase in fatigue following a mooring line failure. However, this state will persist for only six months within the turbine's 20-year lifespan, accounting for 1/40th of its design life. With the implementation of a robust safety factor, these fatigue issues can be effectively mitigated. It is advocated that 'design for failure' is incorporated into a three-leg mooring system design to ensure the risks associated with TetraSpar are ALARP. Five recommendations are suggested for the design phase to ensure the TetraSpar and FOWTs achieve ALARP risk levels considering potential mooring line failure, offering solutions that do not necessitate on-site visits, and ideally creating a system that can endure for six months without intervention, allowing for repairs during the summer campaign for more cost-effective and safer operations.