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Accelerated aging non-linear regression, the Arrhenius formula for the degradation model does not work

Hello everyone,

 

I am currently in the familiarization phase with JMP and watch the tutorial videos that can be booked with the starter license. The video “Stability Analysis” 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 the maximum elongation at three different temperatures (180, 200, 220 ° C) after eight time intervals in days, at 220 ° C only six time intervals. 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 only used a higher activation energy (100 kJ / mol) and a higher temperature starting value (recommended 23 ° C).

In my case, the model recognizes the real starting value (399) in the case of 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, as in the video, it calculates the starting value incorrectly (290), but at least it calculates something and the analysis diagram doesn't make any sense either.

Does anyone have any idea what's going wrong there? 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: The elongations after the measurement time are below 26

 

 

Formula from video

 

 

My formula:

 

 

 

AnalyticsData tableGraphicsOtherWindowsRe: Nicht linearer Regression bei beschleunigter Alterung, die Arrhenius-Formel für das Degradationsmodell funktioniert nicht

Unfortunately, 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 nicht

Hi 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 nicht

Your 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.