Template:Example: Recurrent Events Data Parameteric Air-Condition Example

Example 4
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].

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


 * 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 to Example 4
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 $$\hat{\beta }=1.1976,$$   $$\hat{\lambda }=4.94E-03,$$   $$\hat{q}=0.1344$$.


 * 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: