Large interruptions of power supply in the transmission system have considerable impact on modern society. The goal for the transmission system operator (TSO) is to prevent and mitigate such events with optimal decisions in design, planning, operation and maintenance. Identifying critical power components for system reliability provides one important input to this decision-making. This thesis develops quantitative component reliability importance indices applicable for identifying critical components in real transmission systems. Probabilistic models with component failure statistics are combined with detailed power system models evaluated with the AC power flow technique. In the presented method each system component is assigned three importance indices based on outage events expected probability and consequence to (i) reduced system security margin, (ii) interrupted load supply and (iii) disconnected generation units. By ranking components by each of the three interests, a more complete view of the risks to system reliability can be assessed than if, as traditionally, only (ii) is modelled. The impact on security margin is studied in well established critical transfer sections (CTS) supervised by the TSO. TSOs set the CTSs limits [MW] based on deterministic security criteria, with regard to thermal, voltage level, and system stability limits, and the CTSs' condition at post-contingency state is in the method used as an indicator of the system security margin. The methodology is extended with three indices modified to quantify the component importance for common-cause events initiated by acts of sabotage. The developed methods are applied on a significant part of the Great Britain transmission system, modelling 7000 components and 107 substation layouts. The study includes several load demand scenarios, 200 million initiating outage events and non-functioning protection equipment. The resulting component ranking provides an important input to the TSO's decision-making, and could be implemented as a complement to the existing deterministic N-1 criterion. With the methods applied a TSO can perform further and more detailed assessments on a few critical components in order to enhance system reliability for equipment failures and strengthen the system vulnerability against sabotage. / QC 20110920