7.6 Risk Analysis (Step 4)
181
AND operations within the tree signify that multiple initiating causal events (k)
must occur simultaneously to trigger the event at the next higher level. This operator
therefore reduces the total probability and can be defined as:
P =
k
P k
(7.3)
where P is the total probability and P k is the probability of event k.
OR operations within the tree mean that the occurrence of one of the associated
causal events (k) is sufficient to trigger an event at the next higher level. The total
probability can then be simplified as a sum of the individual event probabilities:
P = 1 −
k
(1 − P k ) ∼ =
k
P k if P << 1
(7.4)
where P is the total probability and P k is the probability of event k.
FTA makes the following assumptions: (1) all events are independent, (2) system
components either perform successfully or fail completely, and (3) failures are
instantaneous (i.e., time delays are omitted). Before using this technique it should
always be checked whether these conditions are met. In cases where these conditions
are not met, FTA can be adapted to include common cause failures.
Event Tree Analysis
Event Tree Analysis (ETA) is a method used to model the propagation of an
initiating event that leads to many possible outcomes. Set up in a fashion that
mirrors the fault tree analysis, in ETA the top event is considered the initiating event.
Starting with the top event, each event following it is conditional on the occurrence
of its precursor event. This form is also represented graphically by a tree.
The probability of occurrence of an outcome N (P N ) resulting from the initiating
top event can be calculated as the product of the probability of the top event (P Top )
and all of subsequent conditional events along the event tree at each step k that leads
to outcome N (P Nk ):
P N = P Top ×
k
P Nk
(7.5)
In this way, an event tree can be used to estimate (1) the probability of occurrence
of potential loss events that might result from a single initiating event, for example,
after the loss of coolant, and (2) the probability of occurrence of consequences
arising from a single loss event, for example, after the release of a hazardous
substance.
Like FTA, event tree analysis primarily uses reliability data to define event probabilities. It also assumes that all events are independent, except for the preceding
outcome branch, and that the system components either perform successfully or fail
completely.
181
AND operations within the tree signify that multiple initiating causal events (k)
must occur simultaneously to trigger the event at the next higher level. This operator
therefore reduces the total probability and can be defined as:
P =
k
P k
(7.3)
where P is the total probability and P k is the probability of event k.
OR operations within the tree mean that the occurrence of one of the associated
causal events (k) is sufficient to trigger an event at the next higher level. The total
probability can then be simplified as a sum of the individual event probabilities:
P = 1 −
k
(1 − P k ) ∼ =
k
P k if P << 1
(7.4)
where P is the total probability and P k is the probability of event k.
FTA makes the following assumptions: (1) all events are independent, (2) system
components either perform successfully or fail completely, and (3) failures are
instantaneous (i.e., time delays are omitted). Before using this technique it should
always be checked whether these conditions are met. In cases where these conditions
are not met, FTA can be adapted to include common cause failures.
Event Tree Analysis
Event Tree Analysis (ETA) is a method used to model the propagation of an
initiating event that leads to many possible outcomes. Set up in a fashion that
mirrors the fault tree analysis, in ETA the top event is considered the initiating event.
Starting with the top event, each event following it is conditional on the occurrence
of its precursor event. This form is also represented graphically by a tree.
The probability of occurrence of an outcome N (P N ) resulting from the initiating
top event can be calculated as the product of the probability of the top event (P Top )
and all of subsequent conditional events along the event tree at each step k that leads
to outcome N (P Nk ):
P N = P Top ×
k
P Nk
(7.5)
In this way, an event tree can be used to estimate (1) the probability of occurrence
of potential loss events that might result from a single initiating event, for example,
after the loss of coolant, and (2) the probability of occurrence of consequences
arising from a single loss event, for example, after the release of a hazardous
substance.
Like FTA, event tree analysis primarily uses reliability data to define event probabilities. It also assumes that all events are independent, except for the preceding
outcome branch, and that the system components either perform successfully or fail
completely.