Reliability and Survival Methods • Degradation • Destructive Degradation
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Destructive Degradation
To measure a product characteristic, sometimes the product must be destroyed. For example, when measuring breaking strength, the product is stressed until it breaks. Regular degradation analysis no longer applies in these situations. You can handle these situations in one of two ways:
•
If your failure time model is a standard one, it may be covered by the Destructive Degradation platform. See the Destructive Degradation section.
•
If you are using custom transformations of the time or response variables and custom nonlinear models, use the Degradation platform. In the launch window, select the Destructive Degradation tab.
Example of Destructive Degradation
The following example fits a custom nonlinear model. The data consist of measurements on the strength of an adhesive bond. The product is stressed until the bond breaks, and the required breaking strength is recorded. Because units at normal use conditions are unlikely to break, the units were tested at several levels of an acceleration factor (temperature). You want to estimate the strength (in newtons) of units after 52 weeks (one year) at use conditions of 25oC.
Complete the Launch Window
1.
Select Help > Sample Data Library and open Reliability/Adhesive Bond.jmp.
2.
Select Analyze > Reliability and Survival > Degradation.
3.
Select the Destructive Degradation tab.
4.
Select Strength and click Y, Response.
5.
Select Weeks and click Time.
6.
Select Degrees and click X.
7.
Select Censor and click Censor.
Completed Launch Window
8.
Click OK.
Define and Fit the Model
1.
Select Lognormal from the menu in the Location Parameter Path Specification panel in the Model Specification outline.
This specifies a lognormal transformation for the response, Strength.
2.
Select Degradation Path Style > Nonlinear Path from the Degradation Data Analysis red triangle menu.
This adds a script window to the report. You insert a script that specifies your model in this window.
3.
Copy the JSL formula below and paste it into the script window under Nonlinear Path:
Parameter(
{b1 = 50, b2 = 50, b3 = -1},
b1 * :Degrees + b2 * Exp( b3 * Sqrt( :Weeks ) )
)
The script defines a model for Strength in terms of parameters b1, b2, and b3. The script specifies initial values for the parameters.
4.
In the text box at the bottom of the report, change Empty to Custom Model.
Nonlinear Path Script
5.
Click Use & Save.
Updated Model Specification Outline
The report is updated and the path for the response is shown. Initial values for the parameters are set to the values specified in the script.
6.
Click Fit Model.
Plot of Fitted Model
The Parameter panel in the Model Specification outline is updated to show the parameter estimates for the fitted model. The model fit is shown in the Overlay plot. You can drag the axes to show the points, as is done in Plot of Fitted Model. The legend identifies the curves.
Obtain Predicted Values and Prediction Intervals
Next, you obtain a predicted value and prediction interval for Strength after 52 weeks at the baseline use condition of 25oC.
1.
Select Prediction Settings from the Degradation Data Analysis red triangle menu.
2.
In the Prediction Settings window:
‒
Enter 25 for Baseline.
‒
Select Prediction Interval from the menu in the Longitudinal Prediction panel.
Prediction Settings
3.
Click OK.
4.
Select the Prediction Graph tab in the report.
5.
Enter 52 in the text box under Prediction Plot.
6.
Click Go.
Prediction Plot at Weeks = 52
The Prediction Plot shows the predicted value and its 95% level prediction interval above the axis label of 25 (Baseline).
7.
From the Prediction Plot red triangle menu, select Save Predictions.
Predicted values for the three values of Degrees and for the desired baseline of 25 degrees are saved to a data table. The predicted strength of the adhesive bond after 1 year at 25o C is 61.96, with a prediction interval of 42.42 to 90.50.