¶ Structure of Event Trees
¶ Description
Figure VII-5 gives the XML representation for the structure of an event tree. This structure makes it possible to walk along the sequences, but not to construct the Boolean formulae associated with each sequence. To do so, we need to fill the structure with instructions. Instructions are actually used for two main purposes:
- To collect formulae or stochastic expressions
- To define flavors of fault trees and probability distributions, i.e., to set values of house events and flag parameters
The collection of a top event consists in a Boolean product of the formula associated with the sequence and a copy of the fault tree rooted with the top event. In the Model Exchange Format, the operation is performed by means of the instruction “collect-formula”. The collection of an expression multiplies the current probability of the sequence by the value of this expression. In the Model Exchange Format, the operation is performed by means of the instruction “collect-expression”.
To give flavors to fault trees, i.e., to change the values of gates, house events, basic events, and parameters, the Model Exchange Format introduces the four corresponding instruction: “set-gate”, “set-house-event”, “set-basic-event”, and “set-parameter”.
Sequences are walked from left to right. Therefore, when a value of an element is changed, this change applies on the current environment and propagates to the right. This default behavior can be changed by using the flag “direction”, which can take either the value “forward” (the default), “backward” or “both”. This feature should be handled with much care.
The flavor given to fault trees, as well as what is collected, may depend on the initial event and the current state of functional events. To do so, the Model Exchange Format provides an if-then-else instruction (the “else” part is optional) and the two expressions “test-initiating-event” and “test-functional-event”. These two instructions have been introduced in the XML representation below. Since the then- and else-branches of the “if-then-else” may contain several instructions, the Model Exchange Format introduces the notion of block of instructions.
test-initiating-event = element test-initiating-event { name }
test-functional-event =
element test-functional-event {
name,
attribute state { Identifier }
}
Finally, some models require linking event trees. A special instruction “event-tree” is introduced for this purpose. It should be used only in sequence definitions, i.e., in end-state.
It is sometimes the case that the same values of house events and parameter flags are used at several places. Such a configuration is called a split-fraction in the event tree linking approach. The Model Exchange Format refers it as a rule, for it is a sequence of instructions.
¶ XML Representation
The RNC schema for the XML representation of instructions is given below
instruction = set | collect | if-then-else | block | rule | link
set = set-gate | set-house-event | set-basic-event | set-parameter
set-gate =
element set-gate {
name,
attribute direction { direction }?,
formula
}
set-house-event =
element set-house-event {
name,
attribute direction { direction }?,
Boolean-constant
}
set-basic-event =
element set-basic-event {
name,
attribute direction { direction }?,
expression
}
set-parameter =
element set-parameter {
name,
attribute direction { direction }?,
expression
}
direction = "forward" | "backward" | "both"
if-then-else = element if { expression, instruction, instruction? }
collect = collect-formula | collect-expression
collect-formula = element collect-formula { formula }
collect-expression = element collect-expression { expression }
block = element block { instruction* }
rule = element rule { name }
link = element event-tree { name }
rule-definition =
element define-rule { name, label?, attributes?, instruction+ }
¶ Example
Consider again the event tree pictured in figure VII-5. The XML representation for the structure of this tree has been given in figure VII-5. Assume that the success branch of the lower fork on system H is a bypass. The XML description for the branches of this example is given in :numref:xml_event_tree_branches. It is easy to verify by traversing this tree by hand so that it produces the expected semantics.
This example does not set any house events or flag parameters. To set a house event for all subsequent sub-tree exploration (including the next fault tree to be collected), it suffices to insert an instruction “set” in front of the instruction “collect”.
<set-house-event name="h1"> <bool value="true"/> </set-house-event>
<collect-formula> <gate name="G"/> </collect-formula>
To set the same house event locally for the next fault tree to be collected, it suffices to set back its value to “false” after gathering of the fault tree.
<set-house-event name="h1"> <bool value="true"/> </set-house-event>
<collect-formula> <gate name="G"/> </collect-formula>
<set-house-event name="h1"> <bool value="false"/> </set-house-event>
The same principle applies to parameters.
Assume now that we want to set the parameters “lambda1” and “lambda2” of some probability distributions to “0.001” if the initiating event was “I1” and the functional event “G” is in the state failure and to “0.002”, otherwise. This goal is achieved by means of an “if-then-else” construct and the “test-initiating-event” expression.
<if>
<and>
<test-initiating-event name="I1"/>
<test-functional-event name="G" state="failure"/>
</and>
<block>
<set-parameter name="lambda1"> <float value="0.001"/> </set-parameter>
<set-parameter name="lambda2"> <float value="0.001"/> </set-parameter>
</block>
<block>
<set-parameter name="lambda1"> <float value="0.002"/> </set-parameter>
<set-parameter name="lambda2"> <float value="0.002"/> </set-parameter>
</block>
</if>
Finally, we could imagine that the sequence S1 is linked to an event tree ET2 if the initiating event was I1 and to another event tree ET3, otherwise. The definition of the sequence S1 would be as follows.
<define-sequence name="S1">
<if>
<test-initiating-event name="I1"/>
<event-tree name="ET2"/>
<event-tree name="ET3"/>
</if>
</define-sequence>