Example: Parametric RDA - Air Condition Unit: Difference between revisions

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{{Banner Weibull Examples}}
<noinclude>{{Banner Weibull Examples}}
<br>
''This example appears in the [https://help.reliasoft.com/reference/life_data_analysis Life data analysis reference]''.
The following table gives the failure times for the air conditioning unit of an aircraft. The observation ended by the time&nbsp;the&nbsp;last failure occurred.&nbsp;[[Appendix: Weibull References|[3]]]  
 
</noinclude>The following table gives the failure times for the air conditioning unit of an aircraft. The observation ended by the time the last failure occurred, as discussed in Cox [[Appendix:_Life_Data_Analysis_References|[3]]].
 
<center><math>\begin{matrix}
<center><math>\begin{matrix}
   \text{50} & \text{329} & \text{811} & \text{991} & \text{1489}  \\
   \text{50} & \text{329} & \text{811} & \text{991} & \text{1489}  \\
Line 8: Line 10:
   \text{268} & \text{544} & \text{950} & \text{1362} & \text{1539}  \\
   \text{268} & \text{544} & \text{950} & \text{1362} & \text{1539}  \\
   \text{290} & \text{732} & \text{955} & \text{1459} & {}  \\
   \text{290} & \text{732} & \text{955} & \text{1459} & {}  \\
\end{matrix}</math></center>
\end{matrix}\,\!</math></center>
:1. Estimate the GRP model parameters using the Type I virtual age option.
 
1. Estimate the GRP model parameters using the Type I virtual age option.
 
2. Plot the failure number and instantaneous failure intensity vs. time with 90% two-sided confidence bounds.
 
3. Plot the conditional reliability vs. time with 90% two-sided confidence bounds. The mission start time is 40 and mission time is varying.


:2. Plot the failure number and instantaneous failure intensity vs. time with 90% two-sided confidence bounds.
4. Using the QCP, calculate the expected failure number and expected instantaneous failure intensity by time 1800.


:3. Plot the conditional reliability vs. time with 90% two-sided confidence bounds. The mission start time is 40 and mission time is varying.
'''Solution'''


:4. Using the QCP, calculate the expected failure number and expected instantaneous failure intensity by time 1800.
Enter the data into a parametric RDA folio in Weibull++. On the control panel, select the '''3''' parameters option and the '''Type I''' setting. Keep the default simulation settings. Click '''Calculate'''.


<br>'''Solution'''
:1. The estimated parameters are <math>\hat{\beta }=1.1976\,\!</math>, <math>\hat{\lambda }=4.94E-03\,\!</math>, <math>\hat{q}=0.1344\,\!</math>.


Enter the data into a parametric RDA&nbsp;folio in Weibull++. Choose '''3''' under Parameters and '''Type I''' under Settings. Keep the default simulation settings.  
:2. The following plots show the cumulative number of failures and instantaneous failure intensity, respectively.


:1. The estimated parameters are <math>\hat{\beta }=1.1976,</math> <math>\hat{\lambda }=4.94E-03,</math> <math>\hat{q}=0.1344</math> .
[[Image:Parametric RDA N(T) plot.png|center|650px]]


:2. The failure number and instantaneous failure intensity are given in the following plots.


[[Image:Parametric RDA N(T) plot.png|thumb|center|400px]]  
[[Image:Parametric RDA Lambda(T) plot.png|center|650px]]  


[[Image:Parametric RDA Lambda(T) plot.png|thumb|center|400px]]
:3. The following plot shows the conditional reliability.


:3. The conditional reliability is plotted below.
[[Image:Parametric RDA Cond R(T) plot.png|center|650px]]


[[Image:Parametric RDA Cond R(T) plot.png|thumb|center|400px]]
:4. Using the QCP, the failure number and instantaneous failure intensity are:


:4. Using QCP, the failure number and instantaneous failure intensity are:
[[Image:QCP N(T).png|center|650px]]


[[Image:QCP N(T).png|thumb|center|400px]]


[[Image:QCP Lambda(T).png|thumb|center|400px]]
[[Image:QCP Lambda(T).png|center|650px]]
[[Category:Weibull++ Examples]]

Latest revision as of 18:52, 18 September 2023

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This example appears in the Life data analysis reference.

The following table gives the failure times for the air conditioning unit of an aircraft. The observation ended by the time the last failure occurred, as discussed in Cox [3].

[math]\displaystyle{ \begin{matrix} \text{50} & \text{329} & \text{811} & \text{991} & \text{1489} \\ \text{94} & \text{332} & \text{899} & \text{1013} & \text{1512} \\ \text{196} & \text{347} & \text{945} & \text{1152} & \text{1525} \\ \text{268} & \text{544} & \text{950} & \text{1362} & \text{1539} \\ \text{290} & \text{732} & \text{955} & \text{1459} & {} \\ \end{matrix}\,\! }[/math]

1. Estimate the GRP model parameters using the Type I virtual age option.

2. Plot the failure number and instantaneous failure intensity vs. time with 90% two-sided confidence bounds.

3. Plot the conditional reliability vs. time with 90% two-sided confidence bounds. The mission start time is 40 and mission time is varying.

4. Using the QCP, calculate the expected failure number and expected instantaneous failure intensity by time 1800.

Solution

Enter the data into a parametric RDA folio in Weibull++. On the control panel, select the 3 parameters option and the Type I setting. Keep the default simulation settings. Click Calculate.

1. The estimated parameters are [math]\displaystyle{ \hat{\beta }=1.1976\,\! }[/math], [math]\displaystyle{ \hat{\lambda }=4.94E-03\,\! }[/math], [math]\displaystyle{ \hat{q}=0.1344\,\! }[/math].
2. The following plots show the cumulative number of failures and instantaneous failure intensity, respectively.
Parametric RDA N(T) plot.png


Parametric RDA Lambda(T) plot.png
3. The following plot shows the conditional reliability.
Parametric RDA Cond R(T) plot.png
4. Using the QCP, the failure number and instantaneous failure intensity are:
QCP N(T).png


QCP Lambda(T).png
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