FussellVeselyImportance

FussellVeselyImportance[rdist,t]

gives the Fussell–Vesely importances for all components in the ReliabilityDistribution rdist at time t.

FussellVeselyImportance[fdist,t]

gives the Fussell–Vesely importances for all components in the FailureDistribution fdist at time t.

Details

  • The Fussell–Vesely importance at time for component is given by where is the probability that at least one minimal cut set containing component has failed at time and is the probability that the system has failed at time . A minimal cut set is a minimal set of components which, if failed, causes the system to fail.
  • The results are returned in the component order given in the distribution list in rdist or fdist.

Examples

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Basic Examples  (3)

Two components connected in series, with different lifetime distributions:

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

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Two components connected in parallel, with different lifetime distributions:

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Use fault tree-based modeling to define the system:

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Scope  (16)

Applications  (3)

Properties & Relations  (6)

See Also

ReliabilityDistribution  FailureDistribution  StructuralImportance  BirnbaumImportance  BarlowProschanImportance  RiskReductionImportance  RiskAchievementImportance  CriticalityFailureImportance  CriticalitySuccessImportance  ImprovementImportance

Introduced in 2012
(9.0)