ImportanceMeasures

R2026b

Importance measures at tree element

Since R2026b

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Description

ImportanceMeasures objects represent the importance measures calculated in Safety Analysis Manager fault tree documents. Each event that contributes to the failure properties calculated at the specified gate has importance measures. For example, if the top-level gate has two input events, the importance measures of the top-level gate includes ImportanceMeasures objects for both events.

Creation

To create ImportanceMeasures objects:

  1. Set the ComputeProperties property of the Gate object to true.

  2. Evaluate a fault tree document by using the evaluate function on a FaultTreeDocument object.

  3. Get the ImportanceMeasures property of the Gate object.

Properties

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This property is read-only.

Element that has the importance measures, represented as an Event object.

This property is read-only.

Birnbaum importance measure, represented as a double. The Birnbaum measure represents how sensitive the failure probability at the Gate object is due to the failure probability changes of the event specified by the Element property.

Data Types: double

This property is read-only.

Fussell-Vesely importance measure, represented as a double. The Fussell-Vesely measure represents the likelihood that the event specified by the Element property contributes to the cutsets of the Gate object.

Data Types: double

This property is read-only.

Criticality importance measure, represented as a double. The criticality measure represents how significant the event specified by the Element property is to the likelihood of the failure at the Gate object.

Data Types: double

Examples

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Create a fault tree document. The fault tree document contains one fault tree. In the fault tree, create seven basic events and three gates under the top-level gate. Specify the failure and event frequency for each event.

myTreeDoc = safetyAnalysisMgr.newDocument("fault-tree");
myFaultTree = myTreeDoc.FaultTrees(1);

myTopGate = myFaultTree.Gates(1);
event1 = createEvent(myTopGate);
event1.FailureModel.Parameters.Q.Value = 0.05;
event1.FailureModel.Parameters.W.Value = 0.05;
event2 = createEvent(myTopGate);
event2.FailureModel.Parameters.Q.Value = 0.1;
event2.FailureModel.Parameters.W.Value = 0.05;
gate1 = createGate(myTopGate);
gate2 = createGate(myTopGate,Type="and");
gate22 = createGate(gate2);

event3 = createEvent(gate1);
event3.FailureModel.Parameters.Q.Value = 0.1;
event3.FailureModel.Parameters.W.Value = 0.1;
event4 = createEvent(gate1);
event4.FailureModel.Parameters.Q.Value = 0.02;
event4.FailureModel.Parameters.W.Value = 0.01;
event5 = createEvent(gate2);
event5.FailureModel.Parameters.Q.Value = 0.2;
event5.FailureModel.Parameters.W.Value = 0.01;
event6 = createEvent(gate22);
event6.FailureModel.Parameters.Q.Value = 0.2;
event6.FailureModel.Parameters.W.Value = 0.2;
event7 = createEvent(gate22);
event7.FailureModel.Parameters.Q.Value = 0.15;
event7.FailureModel.Parameters.W.Value = 0.15;

Evaluate the fault tree document.

evaluate(myTreeDoc)

Each Gate object in the fault tree contains importance measures for each contributing event. To retrieve the importance measures, get the array from the ImportanceMeasures property of the top-level gate.

myImportanceMeasures = myTopGate.ImportanceMeasures
myImportanceMeasures = 

  1×7 ImportanceMeasures array with properties:

    Element
    Birnbaum
    FussellVesely
    Criticality

Algorithms

When you run the evaluate function, the Safety Analysis Manager calculates the Birnbaum, Fussell-Vesely, and Criticality importance measures for each event downstream from this event by using these equations:

Importance MeasureEquation
Birnbaum

BE=P(G|E)−P(G|E¯)

Fussell-Vesely

FVE=P(E)×P(G|E)P(G)

Criticality

CE=P(E)×BEP(G)

The equations use these variables and operations:

  • G — The gate.

  • E — The event.

  • P(E) — The failure probability calculated at E.

  • P(G) — The failure probability calculated at G.

  • P(G|E) — The conditional probability that G occurs if E occurs.

  • P(G|Ē) — The conditional probability that G occurs if E does not occur.

For more information about how these measures are calculated, see [1].

References

[1] Rauzy, Antoine. Probabilistic Safety Analysis with XFTA. The AltaRica Association, 2020.

Version History

Introduced in R2026b

See Also

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Objects

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