gives the criticality failure importances for all components in the ReliabilityDistribution rdist at time t.
- CriticalityFailureImportance is also known as failure criticality or criticality importance factor.
- The criticality failure importance for component is the probability that component has caused system failure, when the system has failed at time .
- The criticality failure importance at time for component is given by , where is the Birnbaum importance for component , is the probability that the component has failed, and is the probability that the system 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:
Consider a special forces team consisting of one person in command, an intelligence officer, and two specialists in each of the areas of weapons, engineering, medical, and communications. Assume the team functions as long as one specialist in each area is available:
Properties & Relations (5)
Failure-based criticality importance can be defined in terms of Probability:
The BirnbaumImportance for all components:
Failure-based criticality importance is related to RiskReductionImportance:
Failure-based criticality importance is related to ImprovementImportance:
Compute the ImprovementImportance:
Wolfram Research (2012), CriticalityFailureImportance, Wolfram Language function, https://reference.wolfram.com/language/ref/CriticalityFailureImportance.html.
Wolfram Language. 2012. "CriticalityFailureImportance." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/CriticalityFailureImportance.html.
Wolfram Language. (2012). CriticalityFailureImportance. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/CriticalityFailureImportance.html