KEVOS® MAKEOS · Maintenance
Arrhenius Acceleration Check (Temperature Acceleration Factor, Equivalent Hours, Test Length)
If I run a life test hotter than the parts see in service, how much faster do temperature-driven failures happen, how many service hours does my test represent, and is it long enough to cover the target life?
Arrhenius temperature acceleration for a life test: the acceleration factor between the use and test temperatures for the activation energy you enter, the equivalent service hours of your test, the test hours needed to represent the target life, and the factor for activation energies 0.1 and 0.2 eV either side, because the result is very sensitive to that value.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Use (service) temperature | °C | Temperature the part runs at in service (at the failure site, not the room). |
| Test (stress) temperature | °C | Temperature during the accelerated test. |
| Activation energy ΔH | eV | Activation energy of the failure mechanism, from your own test data or a source for that mechanism. |
| Test duration | h | Hours each unit spends at the test temperature. |
| Target service life to cover | h | Service life the test should represent. |
What each input means
Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.
What this means: Use (service) temperature
- What it is
- The temperature at the failure site in normal service, such as the junction or the material temperature, not the room air.
- Units and format
- Enter a number in °C: degrees Celsius. The form accepts -200 °C to 2000 °C. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 25 °C as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A higher service temperature lowers the acceleration factor.
- Get it right
- Measure or estimate the part’s own temperature under typical load; a few degrees changes the factor noticeably.
What this means: Test (stress) temperature
- What it is
- The temperature the parts are held at during the accelerated life test.
- Units and format
- Enter a number in °C: degrees Celsius. The form accepts -200 °C to 2000 °C. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 125 °C as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A higher test temperature raises the factor steeply.
- Get it right
- Stay below any temperature that changes the material or starts a different failure mode, such as a glass transition.
What this means: Activation energy ΔH
- What it is
- The activation energy ΔH of the failure mechanism in electron volts, which sets how strongly its rate depends on temperature.
- Units and format
- Enter a number in eV: eV. The form accepts 0.01 eV to 5 eV. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.5 eV as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The factor grows exponentially with it: check the sensitivity table.
- Get it right
- Use a value fitted from your own tests at two or more temperatures, or one published for the same mechanism and material.
What this means: Test duration
- What it is
- The hours each unit spends at the test temperature during the life test.
- Units and format
- Enter a number in h: hours. The form accepts 0.000001 h or more. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1000 h as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Equivalent service hours rise in proportion.
- Get it right
- Count only time at the full test temperature, not warm-up or cool-down.
What this means: Target service life to cover
- What it is
- The service life, in operating hours at the use temperature, that the test is meant to represent.
- Units and format
- Enter a number in h: hours. The form accepts 0.000001 h or more. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 100000 h as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Only moves the pass or fail line and the test hours needed.
- Get it right
- Take it from the product requirement or warranty period converted to operating hours.
Method and formulas
- Arrhenius model: time to fail t_f = A exp(ΔH ÷ kT), with T in kelvin and k Boltzmann’s constant (NIST e-Handbook 8.1.5.1).
- Acceleration factor AF = exp[(ΔH ÷ k)(1 ÷ T_use − 1 ÷ T_test)], k = 8.617333262 × 10⁻⁵ eV/K, T = °C + 273.15.
- Equivalent service hours = AF × test hours; test hours needed = target life ÷ AF.
- Example: acceleration factor 132.66; 1,000 test hours represent 132,660 service hours.
Limitations
- Applies only to failure mechanisms driven by temperature that do not change between use and test temperature; too hot a test can start mechanisms the product never sees in service.
- The activation energy dominates the answer: a 0.1 eV error changes the factor many times over, so use a value measured for the mechanism.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Plan the length of a high-temperature life test
- Convert test hours into equivalent service hours
- Compare test temperatures before committing oven time
Who it is for
- Reliability and test engineers
- Electronics and product engineers
- Quality engineers
What you get
- Acceleration factor
- Equivalent service hours of the test
- Test hours needed for the target life
- Sensitivity to the activation energy
Interpreting the result
- NIST’s example: from 25 °C to 125 °C the factor is about 133 at ΔH = 0.5 eV and about 17,600 at 1.0 eV.
References
- NIST/SEMATECH e-Handbook of Statistical Methods, 8.1.5.1 Arrhenius — https://www.itl.nist.gov/div898/handbook/apr/section1/apr151.htm
Learn the Concepts Behind This Tool
These KEVOS® Library readings explain the method this tool uses, with worked examples.
Method explained here · KEVOS® original book
The Boltzmann factor and the Arrhenius model
In Accelerated Life Testing by the Numbers
What it covers: Why rates rise steeply with temperature, the Arrhenius acceleration factor and its sensitivity to activation energy, averaging a profile, and an activation energy from the wrong part.
Also in Compressing time: what can be accelerated and what cannot
Method explained here · KEVOS® original book
Paper, oil and the life of insulation
In Distribution Transformers by the Numbers
What it covers: Why paper insulation sets a transformer's life, how heat, water and oxygen age it, how to estimate ageing over a daily load cycle, and what oil tests reveal about the paper.
Method explained here · KEVOS® original book
Drive life: capacitors, fans and power cycling
In Variable-Speed Drives by the Numbers
What it covers: How temperature sets the life of a drive's DC link capacitors and cooling fans, how power cycling wears out power modules, and how to combine the parts into a drive reliability and a maintenance plan.
Useful alongside · KEVOS® original book
Adhesives and how they cure
In Adhesive Bonding by the Numbers
What it covers: The main families of engineering adhesives, mixing two-part products, working life and handling strength, cure time against temperature by Arrhenius, and cure and heat resistance.
KEVOS® tools are screening and decision-support utilities. Verify important financial, engineering, safety, legal or operational decisions using appropriate professional standards and your organisation’s approved data.