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

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[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]

Line 28: | Line 28: | ||

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

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

## Revision as of 18:58, 22 February 2012

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

The following table gives the failure times of the air-condition unit of an aircraft. The observation is ended by the time of the last failure [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 Specialized 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.

- 3. The conditional reliability is plotted below.

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