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BUILT-IN MATHEMATICA SYMBOL
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.
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
. - StructuralImportance[bexpr, ...] is defined when UnateQ[bexpr] is True.
Examplesopen all
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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