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AND gate means that the fault (event) occurs if all of the connected subsystems
(immediately below) fail, while with an OR gate, the fault occurs if at least one of the
subsystems (immediately below) fails. This type of modeling easily allows for the
quantification of the risk of failure by the assignment of a probability of occurrence to each
event failure and/or operator action/error at the bottom of the tree. Probabilities then add
(OR gates) or multiply (AND gates) when evaluating the probability of the next higherlevel
event on the tree. This technique assumes independence of the events at each level
of the tree. Dependencies can only be included by incorporating them within the definition
of an event. Often, risk estimation in complex systems is mis-estimated due to the
existence of significant unidentified dependencies. Another limitation of this technique is
the lack of dynamics: the relationships of the tree events are assumed to remain unchanged
with time.
An important notion in a fault tree is that of the minimal cut set, which is the smallest set
of elements such that the system fails (i.e., the top event occurs) if each of the elements
fail. This technique gives a quick view of the possible faults and critical paths of the
system. The main drawbacks of FTA are that failures are assumed to be binary with no
time dependency, and that the analysis does not consider the order of occurrence of events
at any level of the tree ¾ sequential dependency cannot be coped with (in others words,
there is no chronological order of failure occurrences).
On the other hand, an Event Tree Analysis models the possible consequences of a given
hazardous situation (the initiating event). It is, thus, generally used in developing
measures to minimize the consequences of a hazardous situation. An Event Tree Analysis
APPROACHES TO COLLISION RISK ANALYSIS
5-5
is usually represented by branches and generic systems. A generic system is a system or a
function which is designed to reduce the effect of the initiating event, and branches
represent the functioning or malfunctioning of the generic system. The tree starts with the
initiating event, the hazardous situation, from which two branches corresponding to the
functioning/malfunctioning of the first generic system are drawn. Each branch is then split
in two to represent the effect of the second generic system, and so on.... When the
functioning or malfunctioning of any generic system does not influence further
consequences, the branch is terminated. When completed, the tree shows how the
different systems are influenced by the initiating event and the final outcome of the
functioning/malfunctioning of all the generic systems. As in the FTA, only binary events
can be modeled, and only non-recoverable generic event sequences with non-recoverable
initiating events can be described.
Other techniques such as Cause Consequence Diagrams, Probabilistic Safety Assessment,
and Reliability Block Diagrams, all based on FTA or ETA, also belong to this family. The
application of FTA and ETA to collision risk is detailed later in Section 5.2.2.
The Dynamic Assessment Family comprises techniques which can deal with temporal
relationships and model systems where time has an influence on the system behavior.
Examples of these techniques are Discrete State Space Graphs (DSSG), Monte Carlo
Simulations, Discrete Event Simulations, Dynamic Event Tree Analysis, and Hybrid-State
Markov Processes. DSSG models the behavior of a system and its failures by modeling its
discrete states (functional or degraded). States are represented by circles, and transitions
between states by arrows. Depending on the types of distributions of duration times in the
states, analytical expressions may be available for quantification of the state probabilities.
Monte Carlo Simulation allows the construction of a pattern of system responses to an
initiating event. Discrete Event Simulation is another simulation technique to obtain
system responses to an initiating event. However, unlike Monte Carlo simulations, it does
not require expressions for the transition probabilities, but rather a “what-if” description of
the system components. Dynamic Event Tree Analysis is an analytical technique which
uses the probabilistic and physical behavior of a dynamic process for reliability analysis.
The analysis is represented by a tree in which branching can occur at arbitrary discrete
points in time. The state transition modeling is ruled by ordinary differential equations.
Finally, Hybrid-State Markov Processes model quite general systems, as they allow
deterministic and stochastic evolution of a system. This approach requires elaborate
mathematical techniques for numerical evaluation. It is used in the model TOPAZ
　
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