This research has evaluated the rules, guidelines and regulations related to ship vibrations. A historical failure data analysis is carried out to identify associated components, equipment and the areas of defects related to ship vibration problems. Ship Hull Vibration (SHV) is recognised as a major problem onboard ships and the propulsion system is identified as the major contributor to SHV. The current status of ship vibrations is reviewed and possible sources which create SHV are recognised. The major problems identified in this research are associated with risk modelling under circumstances where high levels of uncertainty exist. Following the identification of research needs, this PhD thesis has developed several analytical models for the application of Formal Safety Assessment (FSA). Such mode quently demonstrated by their corresponding case sti vith regard to application of FSA for SHV modelling. Firstly, in this research a generic SHV model is constructed for the purpose of risk estimation based on the identified hazards. The hazards include the SHV effects induced by ship design criteria, failure of components, and different patterns associated with the ship propulsion system (propeller system and machinery) as the major contributors to SHV. Then risk estimation bn is carried out utilising Evidential Reasoning (ER) and a fuzzy rule base.Secondly, ship selection (decision making) is investigated to to select the best ship design based on the risk estimation results of SHV. The risk estimation is carried out using ER, a fuzzy rule base and continuous fuzzy sets. The best ship design is selected by taking into account an ER-based utility ranking approach. Thirdly, combining discrete fuzzy sets and an Analytical Hierarchy Process (AHP) risk estimation is conducted in terms of four risk parameters to select the major causes of component failure and then SHV
