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 , , ... in the Boolean expression bexpr.

DetailsDetails

  • 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 .
  • StructuralImportance[bexpr, ...] is defined when UnateQ[bexpr] is True.

ExamplesExamplesopen allclose all

Basic Examples (4)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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