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

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''' Recurrent Events Data | '''Recurrent Events Data Parametric Air-Condition Example''' | ||

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} | <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 10: | Line 9: | ||

\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. | ||

Line 19: | Line 17: | ||

:4. Using the QCP, calculate the expected failure number and expected instantaneous failure intensity by time 1800. | :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 folio in Weibull++. Choose '''3''' under Parameters and '''Type I''' under Settings. Keep the default simulation settings. | |||

Enter the data into a | |||

:1. The estimated parameters are | :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. | :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 N(T) plot.png|thumb|center|400px]] | ||

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

:3. The conditional reliability is plotted below. | :3. The conditional reliability is plotted below. | ||

[[Image:Parametric RDA Cond R(T) plot.png|thumb|center|400px | [[Image:Parametric RDA Cond R(T) plot.png|thumb|center|400px]] | ||

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

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

## Revision as of 16:17, 8 March 2012

**Recurrent Events Data Parametric Air-Condition Example**

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. [3]

- 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++. Choose **3** under Parameters and **Type I** under Settings. Keep the default simulation settings.

- 1. The estimated parameters are .

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

- 3. The conditional reliability is plotted below.

- 4. Using QCP, the failure number and instantaneous failure intensity are: