gives the risk reduction importances for all components in the ReliabilityDistribution rdist at time t.
- RiskReductionImportance is also known as risk reduction worth.
- The risk reduction importance for component is the factor by which the system unreliability would be decreased if component were perfect. As such, it shows the potential for increase in system reliability by making component better.
- The risk reduction importance at time t for component is given by , where is the probability that the system failed, given that the component never fails, 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 (10)
Any valid ReliabilityDistribution can be used:
ReliabilityDistribution can contain different distribution families:
FailureDistribution Models (9)
Any valid FailureDistribution can be used:
FailureDistribution can contain different distribution families:
Properties & Relations (5)
A system with all components in parallel will have RiskReductionImportance equal to :
For all importances that are not , the RiskReductionImportance approaches 1 as :
Wolfram Research (2012), RiskReductionImportance, Wolfram Language function, https://reference.wolfram.com/language/ref/RiskReductionImportance.html.
Wolfram Language. 2012. "RiskReductionImportance." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/RiskReductionImportance.html.
Wolfram Language. (2012). RiskReductionImportance. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/RiskReductionImportance.html