Order Distribution from Distribution with Units
A system has three components, out of which one is primary and two are redundant. Each component has a lifetime following a WeibullDistribution, with shape parameter 2 and mean lifetime of 885 hours.
In[1]:=
![Click for copyable input](assets.en/order-distribution-from-distribution-with-units/In_114.png)
{sol} = NSolve[
Mean[WeibullDistribution[2, b]] == Quantity[885, "Hours"], b]
Out[1]=
![](assets.en/order-distribution-from-distribution-with-units/O_84.png)
In[2]:=
![Click for copyable input](assets.en/order-distribution-from-distribution-with-units/In_115.png)
\[ScriptD] = WeibullDistribution[2, b] /. sol
Out[2]=
![](assets.en/order-distribution-from-distribution-with-units/O_85.png)
The lifetime of this system can be described as the maximum lifetime of its components.
In[3]:=
![Click for copyable input](assets.en/order-distribution-from-distribution-with-units/In_116.png)
\[ScriptCapitalD] = OrderDistribution[{\[ScriptD], 3}, 3]
Out[3]=
![](assets.en/order-distribution-from-distribution-with-units/O_86.png)
The mean lifetime of the system.
In[4]:=
![Click for copyable input](assets.en/order-distribution-from-distribution-with-units/In_117.png)
Mean[\[ScriptCapitalD]]
Out[4]=
![](assets.en/order-distribution-from-distribution-with-units/O_87.png)
Compare with the computation using ReliabilityDistribution.
In[5]:=
![Click for copyable input](assets.en/order-distribution-from-distribution-with-units/In_118.png)
Mean[ReliabilityDistribution[
comp1 \[Or] comp2 \[Or]
comp3, {{comp1, \[ScriptD]}, {comp2, \[ScriptD]}, {comp3, \
\[ScriptD]}}]]
Out[5]=
![](assets.en/order-distribution-from-distribution-with-units/O_88.png)
Compare probability density function of the lifetime of a single component with that of the system.
show complete Wolfram Language input
Out[6]=
![](assets.en/order-distribution-from-distribution-with-units/O_89.png)