This example of an accelerated destructive degradation model is patterned after an example from Escobar et al. (2003). The data consist of measurements on the strength (measured in newtons) of an adhesive bond. Temperature is considered to be an acceleration factor. The product is stressed until the bond breaks and the required breaking stress is recorded. Because units at normal use conditions are unlikely to break, the units were tested at several levels over a wide range of temperatures. Strength less than 50 newtons is considered failure. You want to estimate the proportion of units with a strength below 50 newtons after 260 weeks (5 years) at use conditions of 35 degrees Celsius.
1.
Select Help > Sample Data Library and open Reliability/Adhesive Bond.jmp.
2.
Select Analyze > Reliability and Survival > Destructive Degradation.
3.
Select Strength and click Y, Response.
4.
Select Weeks and click Time.
5.
Select Degrees and click X.
6.
Select Censor and click Censor.
Notice that the Censor Code is set to Right.
7.
Figure 7.2 Initial Degradation Plot
1.
Select Log for the Y (Strength) Transformation.
2.
Select Sqrt for the Time (Weeks) Transformation.
3.
Select μ = b0x + b1x*f(time) for the Path Definition.
Figure 7.3 Plot Showing Model
4.
Click Generate Report.
Figure 7.4 Report for Basic Model
The estimates of the slope b1 at the three values of Degrees suggest that degradation occurs more quickly at higher temperatures. Failure mechanisms that depend on chemical processes are often well modeled using the Arrhenius model for temperature. For this reason, you now fit a model where an Arrhenius transformation is applied to Degrees, which is measured on a Celsius scale.
5.
Select μ = b0 ± Exp(b1 + b2*Arrhenius(X))*f(time) for the Path Definition.
6.
Select Celsius and click OK.
Figure 7.5 Plot Showing Model with Arrhenius Transformation
7.
Click Generate Report.
Figure 7.6 Report Including Second Model with Arrhenius Transformation
Figure 7.7 Degradation Profiler
The predicted Strength at these settings is 62.25173, with a 95% prediction interval ranging from 50.0318 to 77.4563. Failures are not very likely at these or less extreme settings.
2.
In the Crossing Time Distribution Profiler, set Weeks to 156, Degrees to 35, and Strength to 50.
Figure 7.8 Crossing Time Distribution Profiler
3.
In the Crossing Time Quantile Profiler, set Degrees to 35, Probability to 0.02, and Strength to 50.
Figure 7.9 Crossing Time Quantile Profiler

Help created on 7/12/2018