Acceleration factors

gear used for a rock climbing anchor
Gear for anchor during rock climbing

Temperature acceleration factor for ALT planning (question posted to Linkedin Society of Reliability engineers group, 5/7/12

Hello, can anyone advise me how to calculate temperature acceleration factor for a complex system including cards, RF elements, cables, motors and moving parts? Is the Arrhenius model valid for such systems, or there are more precise models? Thank you!

…and my response…

The acceleration factor equations are commonly tied very closely to a specific failure mechanism. For example, for SAC solder joint fatigue uses the modified Norris Landzberg model. And, for metal migration/corrosion within plastic encapsulated packages Peck’s equation is useful.

Each failure mechanism reacts to stresses differently, some more so than others. Making testing at a system level with accelerated stresses, … , more difficult.

So be careful, unless you know which failure mechanisms are most likely to occur during use and you accelerate appropriately.

If you know that temperature is the stress of interest related to the dominate failure mechanisms, again be careful, as you will quickly find, the activation energy is important and is generally associated with a specific failure mechanism.

And just temperature may not be sufficient – for moving parts, load and frequency of motion may be more useful for acceleration. For connectors and cables, maybe thermal cycling is more important.

If I don’t run a motor with a high temperature and humid environment it may fail due to corrosion. If I simply run it with an unbalanced load, it may wear out the bearing quickly – both lead to failure, yet have completely different acceleration factors (failure mechanisms) and one test or one AF is just not sufficient.

In short, there are more precise models – depending on the failure mechanisms involved.

hope that helps.


Author: Fred Schenkelberg

I am an experienced reliability engineering and management consultant with my firm FMS Reliability. My passion is working with teams to create cost-effective reliability programs that solve problems, create durable and reliable products, increase customer satisfaction, and reduce warranty costs.

6 thoughts on “Acceleration factors”

  1. Thank you for your explanation!
    Your answer is correct theoretically, and I wish I had the resources for testing the system “by the book”. But, as usual in the industry – especially in small companies such as the one I work in – I need to work under limitation of resources. The actual need is to perform Reliability Demonstration Test for the whole system. The required test time to show, with the required confidence level, that the system MTBF (Theta, if you prefer) is sufficient, is too long, when there is a limitation of available number of systems, and time allocated to the test.
    I was looking for possible acceleration factors for this purpose. The reliability prediction pareto shows that the parts most affecting the failure rates are the bearings and motors, and the electrical cards – so I assumed to propose acceleration by increased/unbalanced load for the moving parts, and by temperature for the cards – but I need to decide which temperature acceleration model to use.
    No FMEA was conducted during the design process, so no significant inputs about failure modes are available.
    Any advise under the given circumstances will be welcome with many thanks.


    1. Hi Natasha,

      I fully understand the problem and constraints. Here’s what I suggest – and it’s not strictly by the book, yet closer. Talk to your lead designers about what is expected to fail and under what conditions. Gather information about the use environment, not just the limits, what happens every day. And, make an educated guess or two.

      If your environment includes a very large change in temperature every day (or hour), then thermal cycling may the the stress to focus on and plan your testing acceleration factor around solder joint fatigue (modified Norris Landzberg). If thermal cycling isn’t a big deal (over 20°C per cycle) then consider the thermal exposure and humidity… if in hot humid conditions – then corrosion, metal migration, etc. may play the dominant role. Then plan the testing around Peck’s equation. If both, then do both.

      For motors – they are often easier to get samples and set up a separate test. The motors, if in series, reliability wise – will need a higher reliability target, and more samples or longer run time for demonstration. If you have to use them within the system – then hopefully you can load the motors while doing one or more of the other tests to get the sample size up.

      Unfortunately, there just isn’t a magic temperature acceleration factor for all failure mechanisms – some failures do not care about the temperature, as they fail at the hands of other stresses.

      A little creativity and focus on expected failure mechanisms may move your testing program along.



  2. Hi Fred,

    I had no knowledge about Norris Landzberg and Peck’s equation, I’ll go learn about it.
    Of course, I haven’t assumed to use temperature acceleration for all the failure mechanisms. I just didn’t know any other model for temperature-induced failure mechanisms except Arrhenius.
    I’ll adopt the overall approach you suggested. Thank you!

  3. Hi Fred,

    Useful article, I’m looking at some guidelines on the maximum permissible acceleration factors for stresses such as vibration. I could see in some calculations it is around ~10000. Will it makes sense to have such a acceleration factor?

    Thanks. Rajesh

    1. Hi Rajesh,

      I too would be questioning a 10,000 acceleration factor – and, it all comes down to the failure mechanism and how it behaves as the stress is changed. If the accelerated conditions creates the same failure mechanisms as would occur at normal conditions, then it’s fine. Often this takes some really fundamental understanding of what and how sometime fails.

      Keep asking questions and checking the assumptions.



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