BirnbaumImportance

BirnbaumImportance[rdist,t]

gives the Birnbaum importances for all components in the ReliabilityDistribution rdist at time t.

BirnbaumImportance[fdist,t]

gives the Birnbaum importances for all components in the FailureDistribution fdist at time t.

Details

  • BirnbaumImportance is also known as reliability importance.
  • The Birnbaum importance is the improvement in the reliability that would be gained by replacing a failed component with a perfect component .
  • The Birnbaum importance at time for component is given by where is the probability that the system is working given that the ^(th) component is perfect and is the probability that the system is working given that the ^(th) component has failed.
  • 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  (17)

Applications  (5)

Properties & Relations  (6)

See Also

ReliabilityDistribution  FailureDistribution  StructuralImportance  BarlowProschanImportance  RiskReductionImportance  RiskAchievementImportance  CriticalityFailureImportance  CriticalitySuccessImportance  FussellVeselyImportance  ImprovementImportance

Introduced in 2012
(9.0)