Event tree

In the case of an accident, the final outcome is not known in advance. Different outcomes can occur depending on the initial conditions of the event. The circumstances of the scenario at the time of the accident will decide the final outcome. In the risk analysis procedure it is often necessary to examine a large number of scenarios with different chains of events. Each final event, outcome or subscenario can be assigned a probability of

occurrence as a consequence of the uncertainty in which event will actually occur. In order to structure the possible event sequences arising from an initial event, the event tree approach may be used. An event tree provides a logic graphical description of the possible final events and is therefore a rational method for quantitative risk analysis.

The final events or outcomes in the event tree are denoted subscenarios. The scenario is an aggregation of all subscenarios. Different terminology exists regarding the extent of the scenario. In some literature the scenarios can be defined as the outcomes in the event tree. This is not the case in this thesis. An example of an event tree is presented in Figure 3.1.

The event tree describing evacuation in the case of a fire starts with an initiating event, the initial fire. Different installations or

circumstances which will have an affect on the outcome can be treated as branch events.

At each branch point, different alternatives may occur. For example, an installation such as an automatic fire alarm system will either operate or fail. The alternatives at the branch point affects the following parts of the tree. Each event tree outcome is evidence of the chain of events leading to the final event.

Initial fire Alarm failure yes no Sprinkler failure Emergency door blocked Subscenario 1 Subscenario 2 Subscenario 3 Subscenario 4 Subscenario 5 Subscenario 6 Subscenario 7 Subscenario 8 yes no no yes no yes yes no no yes no yes

Figure 3.1. An event tree for a simple fire risk analysis.

The event tree structures the scenario so that the relevant questions for the analysis can be identified:

• what can happen?

• what is the probability of each subscenario?

• what are the consequences of each subscenario?

Each final outcome, or subscenario, in the event tree has its own set of answers, called the Kaplan and Garrick triplet (Kaplan et al., 1981). A triplet is composed of the three variables, (si, pi, ci),

where i = 1 to n with n equal to the number of subscenarios, i.e. the number of branches in the event tree.

The term si is the event description and pi and ci describe the

probability and consequence of the subscenario. The term ci can, in

some applications, be a vector containing information on different consequences, for example, consequences for the environment, humans or economic loss. Different decision criteria cannot be mixed in one and the same assessment, cf. Chapter 6.

The consequences can be in the form of number of injuries, fatalities or people having their escape routes blocked. The formal derivation of the consequence measure will be further addressed in Chapter 4.

The total risk is the set of all triplets R = {(si, pi, ci)} for the

scenario. In this definition of risk, all information regarding the calculated risk is included. Each subscenario is defined by its probability and its consequence. The set of triplets can be stored as three vectors, one for each component in the triplet.

At each branching point, the possible outcome probabilities for a two-way branch can be described as pfailure and

psuccess = 1.0 - pfailure. The probability of the final subscenario, pi,

for each branch, is simply the product of the branch probabilities leading to that subscenario. The probability of the initial event,

pinitial, should also be included in pi.

It is sometimes convenient to separate the probability of the initiating event and the probabilities of the events described by the event tree. The probability of each subscenario without,

consideration of the initial event probability, can be denoted pET,i.

The total subscenario probability can then be written

p_i = p_initial⋅p_{ET i}, [3.1]

The probability pinitial can be omitted when comparative studies are

performed, when this probability is the same for all cases being investigated. The only differences then originate from different scenario descriptions, i.e. different event trees. The probability pi

in the triplet is replaced by pET,i for comparative studies. The sum

of the pET,i can be written

p_{ET i}

n

, .

As a consequence of this, the sum of the pi can be written

pi pinitial n

=

∑

Further refinements of the quantity pi can be made to include, for

example, variable uncertainty. This will be further described in Chapter 6.

The idea of triplets can also be used for situations where variables are subject to uncertainty. Inclusion of variable uncertainty makes it possible to answer the question "How certain is the calculated risk?"

Usually, both the outcome probability of the subscenario, pi, and

the description of the consequences, ci, are subject to some

uncertainty. Information concerning the state of knowledge of the variables must be included in both pi and ci. The set of triplets can

then be written R = {(si, pi(φi), ζi(ci))} using the notation of Kaplan

and Garrick. The state of knowledge in the probability of each subscenario is expressed by assuming that it follows a probability density function, pi(φi), instead of being a single value. In the same

way, the consequences can be subject to uncertainty which is expressed by the function ζi(ci).