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BUILT-IN MATHEMATICA SYMBOL
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 t for component
is given by 
where 
is the probability that the system is working given that the 
component is perfect and 
is the probability that the system is working given that the 
component has failed. - The results are returned in the component order given in the distribution list in rdist or fdist.
Examplesopen all
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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