CriticalitySuccessImportance

CriticalitySuccessImportance[rdist,t]

gives the criticality success importances for all components in the ReliabilityDistribution rdist at time t.

CriticalitySuccessImportance[fdist,t]

gives the criticality success importances for all components in the FailureDistribution fdist at time t.

Details

  • CriticalitySuccessImportance is also known as criticality importance factor.
  • The criticality success importance for component is the probability that component is the component that contributes to system success, given that the system is working.
  • The criticality success importance at time for component is given by , where is the Birnbaum importance for component , is the probability that the component is working, and is the probability that the system is working.
  • The results are returned in the component order given in the distribution list in rdist or fdist.

Examples

open allclose all

Basic Examples  (3)

Two components connected in parallel, with different lifetime distributions:

In[1]:=
Click for copyable input

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

In[2]:=
Click for copyable input
Out[2]=
In[3]:=
Click for copyable input
Out[3]=

Both serial components are contributing to a working system:

In[1]:=
Click for copyable input
In[2]:=
Click for copyable input
Out[2]=

Use fault tree-based modeling to define the system:

In[1]:=
Click for copyable input
In[2]:=
Click for copyable input
Out[2]=
In[3]:=
Click for copyable input
Out[3]=

Scope  (17)

Applications  (3)

Properties & Relations  (3)

See Also

ReliabilityDistribution  FailureDistribution  StructuralImportance  BirnbaumImportance  BarlowProschanImportance  RiskReductionImportance  RiskAchievementImportance  CriticalityFailureImportance  FussellVeselyImportance  ImprovementImportance

Introduced in 2012
(9.0)