BUILT-IN MATHEMATICA SYMBOL

# CriticalityFailureImportance

CriticalityFailureImportance[rdist, t]
gives the criticality failure importances for all components in the ReliabilityDistribution rdist at time t.

CriticalityFailureImportance[fdist, t]
gives the criticality failure importances for all components in the FailureDistribution fdist at time t.

## DetailsDetails

• CriticalityFailureImportance is also known as failure criticality or criticality importance factor.
• The criticality failure importance for component is the probability that component has caused system failure, when the system has failed at time .
• The criticality failure importance at time for component is given by , where is the Birnbaum importance for component , is the probability that the component has failed, and is the probability that the system has failed.
• The results are returned in the component order given in the distribution list in rdist or fdist.

## ExamplesExamplesopen allclose all

### Basic Examples (3)Basic Examples (3)

Two components connected in series, with different lifetime distributions:

The result is given in the same order as the distribution list in ReliabilityDistribution:

 Out[8]=
 Out[9]=

Both parallel components are contributing to system failure:

 Out[2]=

Use fault tree-based modeling to define the system:

 Out[2]=
 Out[3]=

### Properties & Relations (5)Properties & Relations (5)

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