StructuralImportance

StructuralImportance[rdist]

gives the structural importances for all components in the ReliabilityDistribution rdist.

StructuralImportance[fdist]

gives the structural importances for all components in the FailureDistribution fdist.

StructuralImportance[bexpr,{x1,x2,}]

gives the structural importance for the components x1, x2, in the Boolean expression bexpr.

Details

  • StructuralImportance is also known as Birnbaum's structural importance.
  • The structural importance for component is the fraction of the system states in which component is working, where a failure of component will result in a failure of the system.
  • For StructuralImportance[fdist] and StructuralImportance[rdist], the results are returned in the component order given in the distribution list in rdist or fdist.
  • For StructuralImportance[bexpr,{x1,x2,}], the results are returned in the order {x1,x2,}.
  • StructuralImportance[bexpr,] is defined when UnateQ[bexpr] is True.

Examples

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Basic Examples  (4)

Two components connected in series:

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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:

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Use the structure function directly, without lifetime distributions:

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Use fault tree-based modeling to define the system:

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Scope  (18)

Applications  (4)

Properties & Relations  (4)

Neat Examples  (1)

See Also

ReliabilityDistribution  FailureDistribution  BirnbaumImportance  BarlowProschanImportance  RiskReductionImportance  RiskAchievementImportance  CriticalityFailureImportance  CriticalitySuccessImportance  FussellVeselyImportance  ImprovementImportance

Introduced in 2012
(9.0)