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 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.

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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