Example of Piecewise Weibull NHPP Change Point Detection
This example shows change point detection in a piecewise NHPP Weibull model with data in the Time in Dates format. The data are fixes to a braking system. The Date column gives the dates when Fixes, given in the second column, were implemented. For these data, the failure times are known. Note that the Date column must be in ascending order.
The test start time is the first entry in the Date column, 09/29/2011, and the corresponding value for Fixes is set at 0. This is needed in order to convey the start time for testing. If there had been a nonzero value for Fixes in this first row, the corresponding date would have been treated as the test start time. However, the value of Fixes would have been treated as 0 in the analysis.
The test termination time is given in the last row as 05/31/2012. Because the value in Fixes in the last row is 0, the test is considered to be time terminated on 5/31/2012. If there had been a nonzero value for Fixes in this last row, the test would have been considered failure terminated.
1. Select Help > Sample Data Folder and open Reliability/BrakeReliability.jmp.
2. Select Analyze > Reliability and Survival > Reliability Growth.
3. Select the Dates Format tab.
4. Select Date and click Timestamp.
5. Select Fixes and click Event Count.
6. Click OK.
7. Click the Reliability Growth red triangle and select Fit Model > Crow AMSAA.
The Cumulative Events plot in the Observed Data report updates to show the model. The model does not seem to fit the data very well.
Figure 11.25 Cumulative Events Plot with Crow AMSAA Model
8. Click the Reliability Growth red triangle and select Fit Model > Piecewise Weibull NHPP Change Point Detection.
The Cumulative Events plot in the Observed Data report updates to show the piecewise model fit using change-point detection. Both models are shown in Figure 11.26. Though the data are rather sparse, the piecewise model seems to provide a better fit to the data.
Figure 11.26 Cumulative Events Plot with Two Models
