Traditional solution of fault trees involves the determination of so-called minimal cut sets. Minimal cut sets are all the unique combination of component failures that can cause system failure. Specifically, a cut set is said to be a minimal cut set if, when any basic event is removed from the set, the remaining events collectively are no longer a cut set [10]. As an example, consider the fault tree shown in Figure 10.46. The system will fail if {1, 2, 3 and 4 fail} or {1, 2 and 3 fail} or {1, 2 and 4 fail}.
Figure 10.46: Minimal cut set example.
All of these are cut sets. However, the one including all components is not a minimal cut set because, if 3 and 4 are removed, the remaining events are also a cut set. Therefore, the minimal cut sets for this configuration are {1, 2 ,3} or {1, 2, 4}. This may be more evident by examining the RBD equivalent of Figure 10.46, as shown in Figure 10.47.
Figure 10.47: RBD of the fault tree shown in Figure 10.46.
BlockSim does not use the cut sets methodology when analyzing fault trees. However, interested users can obtain these cut sets for both fault trees and block diagrams with the command available in the Tools menu.
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