gives the Birnbaum importances for all components in the ReliabilityDistribution rdist at time t.
- 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.
Examplesopen allclose all
Basic Examples (3)
The result is given in the same order as the distribution list in ReliabilityDistribution:
ReliabilityDistribution Models (9)
Any valid ReliabilityDistribution can be used:
FailureDistribution Models (8)
Any valid FailureDistribution can be used:
Properties & Relations (6)
BirnbaumImportance can be defined in terms of probability:
Compare with definition of CriticalityFailureImportance:
Compare with definition of ImprovementImportance:
StructuralImportance is Birnbaum importance with component reliabilities :
Wolfram Research (2012), BirnbaumImportance, Wolfram Language function, https://reference.wolfram.com/language/ref/BirnbaumImportance.html.
Wolfram Language. 2012. "BirnbaumImportance." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/BirnbaumImportance.html.
Wolfram Language. (2012). BirnbaumImportance. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/BirnbaumImportance.html