BUILT-IN MATHEMATICA SYMBOL

# RiskReductionImportance

RiskReductionImportance[rdist, t]
gives the risk reduction importances for all components in the ReliabilityDistribution rdist at time t.

RiskReductionImportance[fdist, t]
gives the risk reduction importances for all components in the FailureDistribution fdist at time t.

## DetailsDetails

• 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 would be 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.

## ExamplesExamplesopen allclose all

### Basic Examples (3)Basic Examples (3)

Two components connected in series, with different lifetime distributions:

The result is given in the same order as the distribution list in ReliabilityDistribution:

 Out[12]=
 Out[13]=

By improving a parallel component, the system reliability can be improved infinitely:

 Out[2]=

Use fault tree-based modeling to define the system:

 Out[2]=
 Out[3]=

### Properties & Relations (5)Properties & Relations (5)

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