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

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].

[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 Specialized Folio in Weibull++. Choose 3 under Parameters and Type I under Settings. Keep the default simulation settings.

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 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: