Accelerated aging non-linear regression, Arrhenius formula for degradation model does not workHello everyone,
I am currently in the induction phase at JMP and am watching the tutorial videos that can be booked with the starter license. The "Stability Analysis" video is about determining the best-before date for a drug using accelerated aging.
I tried to transfer this calculation method to our material (rubber), which should actually be possible.
I have measurements of maximum strain at three different temperatures (180, 200, 220°C) after eight time intervals in days, at 220°C only six time intervals. However, the Arrhenius formula of the degradation model shown in the video doesn't work for me and I can't explain why (see formulas below). I took the table variables and parameters from the video, I just used a higher activation energy (100 kJ/mol) and a higher temperature start value (recommended 23°C).
For me, the model recognizes the real starting value (399) with non-linear adjustment, but nothing else. In the video, a theoretical decay is first calculated in the Degradation Model column and based on that I believe the real activation energy of the decay, that doesn't work for me. If I set the activation energy to 10, like in the video, it miscalculates the starting value (290), but at least it calculates something and the analysis chart doesn't make sense either.
Does anyone have an idea what's going wrong? Please no JSL scripts as an answer, I'm not that far yet! 
Thanks in advance!
Adjustment with EA = 100 Adjustment with EA = 10
My data: Under 26 are the strains after the measurement time
Formula from video
My formula:
Quality and Process EngineeringWindowsRe: Nicht linearer Regression bei beschleunigter Alterung, die Arrhenius-Formel für das Degradationsmodell funktioniert nichtAfter consulting with the developer, we have devised a simple solution. Use the middle experimental temperature (200°C in your case) for the reference temperature instead of the use condition. Fit the model using the original starting values, from the beginning. Then extrapolate back to the use condition (23°C in your case). It should look like this using the Nonlinear platform. You should not experience the instability of the estimates this way. I get identical estimates in the Degradation platform now, too.
I updated my data table with these changes. It is attached below.
Re: Nicht linearer Regression bei beschleunigter Alterung, die Arrhenius-Formel für das Degradationsmodell funktioniert nichtUnfortunately, nonlinear regression can depend heavily on the starting values, so using heuristics about the situation can be helpful. I doubt that the EA is as large as 100, so EA = 10 is likely a better choice. The rate of change d is a much larger here than 0.01. What if you try d = 10 for a starting value?
You might also investigate another platform for this kind of analysis. See the Help chapter about the Degradation Platform.
Re: Nicht linearer Regression bei beschleunigter Alterung, die Arrhenius-Formel für das Degradationsmodell funktioniert nichtHi Mark,
thanks for the hint. I've already tried to set EA to 10, as I described that in my problem description. Then the starting value is calculated wrong then and the analysis diagram doesn't make any sense. I also tried to fit my data with EA =1, that doesn't help. I tried to use the degradation platform under the analysis funktion, but there I can't find an Arrhenius model, maybe it is there and I don't recognize it as such.
Re: Nicht linearer Regression bei beschleunigter Alterung, die Arrhenius-Formel für das Degradationsmodell funktioniert nichtYour rate of change is faster than the example in the course, so I also suggested simultaneously using a larger starting value for d.
I entered your data into a data table and added the formula for the nonlinear model. JMP seems to struggle to find a good fit. The convergence is highly dependent on the starting values.
I also tried using the Degradation platform. I saved a script for both Nonlinear and Degradation in the data table.
You should report this issue to JMP Technical Support (support@jmp.com) and provide this data table for investigation.
Re: Nicht linearer Regression bei beschleunigter Alterung, die Arrhenius-Formel für das Degradationsmodell funktioniert nichtI did some more investigation and also reported this case to the developers. They found that there is a large numerical instability due to the large difference between the use condition and the experimental temperatures. You can see the effect in both the high correlation between the d and ea parameters, and the parameter profiler. You can change ea and then change d to get essentially the same SSE, so there is no stable convergence.
It is posible that this model is not good for your data. The best result that I got still exhibited nonlinear residual patterns. It might be that the assumptions of this model are violated. You could try transforming the response or the time to see if that change improves the stability of the fit. You could try another model, like the Eyring model with two factors.
Re: Nicht linearer Regression bei beschleunigter Alterung, die Arrhenius-Formel für das Degradationsmodell funktioniert nichtHi Mark,
To change the application temperature from 23°C more close to the measurement temperatures led to the goal. Indeed, the application temperature is between 180 and 220°C. Thanks for finding my mistake!
Re: Nicht linearer Regression bei beschleunigter Alterung, die Arrhenius-Formel für das Degradationsmodell funktioniert nichtIt is easy to make a simple mistake in a complicated analysis like this one. I learned something, too.
