Template:Example: Recurrent Events Data Parameteric Air-Condition Example: Difference between revisions

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'''Recurrent Events Data Parametric Air-Condition Example'''
#REDIRECT[[Example:_Parametric_RDA_-_Air_Condition_Unit]]
 
The following table gives the failure times of the air-condition unit of an aircraft. The observation ended by the time of the failure occurred. [[Appendix: Weibull References|[3]]]
<center><math>\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></center>
: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.
 
<br>'''Solution'''
 
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.
 
:1. The estimated parameters are <math>\hat{\beta }=1.1976,</math> <math>\hat{\lambda }=4.94E-03,</math> <math>\hat{q}=0.1344</math> .
 
: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|thumb|center|400px]]
 
:3. The conditional reliability is plotted below.
 
[[Image:Parametric RDA Cond R(T) plot.png|thumb|center|400px]]
 
:4. Using QCP, the failure number and instantaneous failure intensity are:
 
[[Image:QCP N(T).png|thumb|center|400px]]
 
[[Image:QCP Lambda(T).png|thumb|center|400px]]

Latest revision as of 04:33, 31 July 2012

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