Fault Tree Analysis
Worked Example - Pressure Regulating Installation
This example uses a simple pressure regulating installation to illustrate how fault tree analysis is used to how events can lead to the top event.
The diagram represents the configuration of the installation:
There are many states that can exist for this installation, but some may have dangerous consequences. For this installation, overpressure downstream has been identified as having the most potential to cause harm. The fault tree will be used to determine which events will lead to the top event and will be the basis of calculations to determine the probability of this event.
The first stage is to determine what events directly cause over pressure. These are:
- • Failure in the open position of the working stream
- OR
- • Failure in the open position of the standby stream
The first 'gate' in the tree can now be drawn:
The diagram shows an 'OR' gate signifying that one event OR the other can cause the top event.
Stage two is to determine those events that contribute to failure of the working and standby streams
Two events contribute to stream 1 failing open:
- • Failure in the open postion of the regulator
- AND
- • Failure in the open postion of the slam shut valve
Stream 2 is similar to Stream 1 and the second layer can now be drawn:
Here we can see an 'AND' gate which signifies that both the regulator AND the slam shut valve must fail open to to cause failure of the stream.
Finally in this example, the basic events that lead to failure are added:
The basic events are shown as a circle and represent the lowest level of analysis.
The diamond symbol used to show 'slam shut failure' is an Undeveloped event, that is to say an event that could be further broken down if required.
Calculations
With the fault tree complete, information can be added for calculation of probabilities.
Here, the probability in a year of each basic event is given, so the overall probability is of the top event occurring in a year. The inverse of this is the frequency in years of the top event.
In this example, the probability of the top event is calculated at 1.5x10-5 in a year or once every 66,666 years. Note: There are several combinations of events that have different probabilities, however, the worst case (highest probability) is of most interest.
Data
To enable calculation of probabilities, information on failure rates is required. This can be from the organisations failure data and operating history, or where this information is not available, some generic data can often be obtained from the public sector.
