Page 408 - Offshore Electrical Engineering Manual

Fault Trees 395

Having defined the top event, each combination event is defined by asking the
following questions:

1. ‘What events taken singly will directly result in the event under consideration?’
These events are connected to the event under consideration by an OR gate.
2. ‘What combination of events will directly result in the event under consider-
ation?’ These events are connected to the event under consideration by an AND
gate.

By definition, all combination events will be the consequence of events drawn
below them and connected in some way via logic gates. The fault tree is complete
when all combination events are shown to be the cause of two or more basic events.
When the fault tree has been drawn, various methods can be applied to it to identify
problems in the system that it represents, as described in the following section.

COMMON MODE FAILURE IDENTIFICATION

If the same event appears in several places on the fault tree, common mode failures
may be identified. Some examples of common mode failures are as follows:

(a) Fire in a switchroom leading to the loss of two or more distribution routes.
(b) Fuel gas system fault leading to all main generators failing.
(c) Loss of hazardous area ventilation leading to shutdown of all main oil line
pumps and/or all gas export compressors.

QUALITATIVE ANALYSIS

This can be carried out by inspecting a simple fault tree to identify any minimal cut
sets. These sets consist of a group of basic events which will cause the top event to
occur if and only if they exist simultaneously. Boolean reduction may also be used,
provided there are no ‘exotic’ logic gates such as those with a sequential or timed
inhibit function.

QUANTITATIVE ANALYSIS
There are two main methods of analysing a fault tree quantitatively.

Evaluation Using Event Probabilities
This method is used when the event failure data is available in terms of probabilities.
Where two events are output through an AND gate (see Fig. 8.1.5), the failure
probabilities may be added as follows:
P (a · b) = P (a) · P (b) where (a · b) represents a AND b
Where two events are output through an OR gate, the resultant probability of
failure is as follows:
P (a + b) = P (a) + P (b) − P (a) P (b) where (a + b) represents a OR b