Probabilistic Safety Assessment (PSA) is a systematic and comprehensive methodology to evaluate risks associated with a complex engineered technological entity. The information provided by PSA has been increasingly implemented for regulatory purposes but rarely used in providing information for operation and maintenance activities. As one of the key parts in PSA, Fault Tree Analysis (FTA) attempts to model and analyze failure processes of engineering and biological systems. The fault trees are composed of logic diagrams that display the state of the system and are constructed using graphical design techniques. Risk Importance Measures (RIMs) are information that can be obtained from both qualitative and quantitative aspects of FTA. Components within a system can be ranked with respect to each specific criterion defined by each RIM. Through a RIM, a ranking of the components or basic events can be obtained and provide valuable information for risk-informed decision making. Various RIMs have been applied in various applications. In order to provide a thorough understanding of RIMs and interpret the results, they are categorized with respect to risk significance (RS) and safety significance (SS) in this thesis. This has also tied them into different maintenance activities. When RIMs are used for maintenance purposes, it is called risk-informed maintenance. On the other hand, the majority of work produced on the FTA method has been concentrated on failure logic diagrams restricted to the direct or implied use of AND and OR operators. Such systems are considered as coherent systems. However, the NOT logic can also contribute to the information produced by PSA. The importance analysis of non-coherent systems is rather limited, even though the field has received more and more attention over the years. The non-coherent systems introduce difficulties in both qualitative and quantitative assessment of the fault tree compared with the coherent systems. In this thesis, a set of RIMs is analyzed and investigated. The 8 commonly used RIMs (Birnbaum‘s Measure, Criticality Importance Factor, Fussell-Vesely Measure, Improvement Potential, Conditional Probability, Risk Achievement, Risk Achievement Worth, and Risk Reduction Worth) are extended to non-coherent forms. Both coherent and non-coherent forms are classified into different categories in order to assist different types of maintenance activities. The real systems such as the Steam Generator Level Control System in CANDU Nuclear Power Plant (NPP), a Gas Detection System, and the Automatic Power Control System of the experimental nuclear reactor are presented to demonstrate the application of the results as case studies. / UOIT