Issue 37, March 2004

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 (i.e. k-out-of-n redundancy), are the most basic types of gates in classical fault tree analysis. These basic gates are explicitly provided for in BlockSim FTI and are described in this article along with their BlockSim implementations. Additional gates will be introduced in next month's issue of the HotWire.

AND Gate

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.

AND Gate Example

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.

Figure 1: Fault tree representation

Figure 2: Reliability block diagram representation

The reliability equation for either configuration is:

OR Gate

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.

OR Gate Example

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.

Figure 3: Fault tree representation

Figure 4: Reliability block diagram representation

The reliability equation for either configuration is:

Voting OR Gate

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.

Figure 5: Illustration of a 2-out-of-4 Voting OR gate

Figure 6: Equivalent representation of the 2-out-of-4 Voting OR gate utilizing a 3-out-of-4 node

Expanding the Classical Voting OR Gate

Classical Voting OR gates have no properties and cannot fail or be repaired (i.e. they cannot be an event themselves). In BlockSim FTI, Voting OR gates behave like nodes in an RBD; thus, they can also fail and be repaired just like any other event. By default, when a Voting OR gate is inserted into an FTD within BlockSim, the gate is set so that it cannot fail (classical definition). However, this property can be modified by the user to allow for additional flexibility.

Classic Voting OR Gate Example

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.

Figure 7: Fault tree representation

Figure 8: Reliability block diagram representation

The reliability equation for either configuration is:

The above equation assumes a classical Voting OR gate (i.e. the voting gate itself cannot fail). If the gate can fail then the equation is modified as follows:

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.

Combining Basic Gates

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.

Figure 9: Sample FTD utilizing different gates

Figure 10: RBD representation of the FTD 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 (i.e. they cannot fail).

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