Accelerated life testing (ALT): extrapolating to use conditions

Accelerated life testing runs units at higher-than-normal stress so they fail in weeks instead of years, then extrapolates the result back to normal operating conditions. You can't wait ten years to learn whether a component lasts ten years — so you raise the temperature, voltage, or load until failures arrive on a testable timescale, fit a model that ties life to stress, and read off the life you'd see at the use level.

The whole method rests on one assumption: that raising the stress speeds up the same failure mechanism without introducing a new one. Bake a capacitor too hot and you stop learning about its field failures and start learning about a mode that never happens in service. Chosen well, though, ALT is the only practical way to characterise long-lived products.

The life-stress relationship

An ALT model has two parts: a life distribution (Weibull, lognormal, …) that describes the scatter in failure times at any fixed stress, and a life-stress relationship L(S) that says how the distribution's characteristic life shifts as the stress S changes. The shape stays the same across stresses; the scale slides. The common relationships:

• Arrhenius — for thermal ageing, driven by absolute temperature T (in kelvin):

  L(T) = A · exp(Ea / (k · T))
  

  where Ea is the activation energy and k is Boltzmann's constant. Life falls exponentially as temperature rises.

• Inverse power law — for voltage, load, or pressure:

  L(V) = A · V^(−n)
  

  Doubling the stress cuts life by a factor of 2ⁿ.

• Eyring — a thermodynamically-derived thermal model, a physically grounded alternative to Arrhenius, and the base for combined temperature-plus-another- stress models.

For two stresses at once (temperature and voltage, temperature and humidity), dual relationships such as temperature-nonthermal and the dual-exponential (Peck) model extend the same idea.

The acceleration factor

The single most useful number ALT produces is the acceleration factor — how much faster the clock runs at the test stress than at use:

AF = L(use) / L(test)

If a unit's characteristic life is 200 hours at the test stress and 20,000 hours at the use stress, AF = 100: one hour on the bench buys a hundred hours of field life. It also tells you how to plan the test — to demonstrate a 10,000-hour use life at AF = 100, you need units to survive ~100 hours on test.

A worked temperature example

Suppose you test a component at three temperatures and fit an Arrhenius-Weibull model, getting these characteristic lives:

 60 °C (333 K):  ~12,000 h
 85 °C (358 K):  ~3,200 h
110 °C (383 K):  ~950 h

Life is dropping by roughly 3–4× per 25 °C — the signature of thermal acceleration. The fitted Arrhenius line lets you extrapolate below the tested range to a 40 °C (313 K) use condition, giving a use-level characteristic life and, from the acceleration factor against your test point, exactly how much lab time represents a given field life. Because the Weibull shape β is shared across temperatures, the whole reliability curve — not just the mean — transfers to the use condition, so you can read B10 life, mean life, and reliability at any mission time at 40 °C.

Reading the fit critically

Two checks separate a trustworthy ALT model from a plausible-looking one. First, plot the failures at each stress on the distribution's probability paper: a good fit shows the points at every stress level hugging parallel straight lines — parallel because the shape is shared, straight because the distribution is right. Fanning or curving lines mean the shape isn't really constant across stress, and the extrapolation is on thin ice. Second, sanity-check the implied physics: an Arrhenius activation energy far outside the 0.3–1.5 eV range that most mechanisms fall in is a warning that you may be fitting more than one failure mode.

Frequently asked questions

What is accelerated life testing?

A method that subjects units to stress levels higher than normal use — temperature, voltage, load, humidity — so they fail quickly, then fits a life-stress model to extrapolate the failure behaviour back to normal conditions. It's how you characterise the reliability of long-lived products without waiting for their full life.

What is the acceleration factor?

The ratio of life at the use stress to life at the test stress, AF = L(use)/L(test). It's the multiplier between bench time and field time: an AF of 50 means each test hour represents 50 hours of service life.

Which life-stress model should I use?

Match the model to the dominant stress and mechanism: Arrhenius (or Eyring) for temperature-driven ageing, inverse power law for voltage/load/pressure, and a dual model when two stresses act together. The failures on probability paper and the physical plausibility of the fitted parameters tell you whether the choice holds.

How is ALT different from an ordinary life-data fit?

An ordinary fit uses failures at a single operating condition. ALT fits failures gathered across several elevated stresses and adds a life-stress relationship, so it can extrapolate to a use level you never actually tested — the thing a single-condition fit cannot do.