Reliability HotWire |
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Reliability Basics | |||||||||

Overview of Fault Tree
Gates (Part I)
Gates are the logic symbols that interconnect
contributory events and conditions in a fault tree diagram. The AND and OR
gates, as well as Voting OR gates in which the output event occurs if a
certain number of the input events occur (
In an AND gate, the output event occurs if all input events occur. In system reliability terms, this implies that all components must fail (input) in order for the system to fail (output). When using RBDs, the equivalent is a simple parallel configuration.
Consider a system with two components: A and B. The system fails if both A and B fail. The next two figures show both the FTD and RBD representations of the system.
The reliability equation for either configuration is:
In an OR gate, the output event occurs if at least one of the input events occurs. In system reliability terms, this implies that if any component fails (input) then the system will fail (output). When using RBDs, the equivalent is a series configuration.
Consider a system with three components: A, B and C. The system fails if either A, B or C fails. The next two figures show both the FTD and RBD representations of the system.
The reliability equation for either configuration is:
In a Voting OR gate, the output event occurs if a certain number of the input events occur. In system reliability terms, this implies that if any k-out-of-n components fail (input) then the system will fail (output). The equivalent RBD construct is a node and it is similar to a k-out-of-n parallel configuration with a distinct difference, as discussed next. To illustrate this difference, consider a fault tree diagram with a 2-out-of-4 Voting OR gate, as shown in Figure 5. In this diagram, the system will fail if any two of the blocks below fail. Equivalently, this can be represented by the RBD shown in Figure 6 utilizing a 3-out-of-4 node. In this configuration, the system will not fail if three out of four components are operating, but will fail if more than one fails. In other words, the fault tree looks at k-out-of-n failures for the system failure while the RBD looks at k-out-of-n successes for system success.
Classical Voting OR
gates have no properties and cannot fail or be repaired (
Consider a system with three components: A, B and C. The system fails if any two components fail. The next two figures show both the FTD and RBD representations of the system.
The reliability equation for either configuration is:
The above equation assumes a
classical Voting OR gate (
Note that while both the gate and the node are 2-out-of-3, they represent different circumstances. The Voting OR gate in the fault tree indicates that if two components fail then the system will fail; while the node in the reliability block diagram indicates that if at least two components succeed then the system will succeed.
As in reliability block diagrams where different configuration types can be combined within the same diagram, fault tree analysis gates can also be combined to create more complex representations. As an example, consider the fault tree diagram shown in Figure 9.
A fault tree diagram is always
drawn in a top-down manner with the lowest item being a basic event block.
Classical fault tree gates have no properties ( | |||||||||

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