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Accelerated life testing formulas.

Point-model equations for translating exposure between use and accelerated conditions, with units and mechanism boundaries made explicit.

Acceleration factor and equivalent exposure

AF = modeled life at use condition / modeled life at test conditionEquivalent accelerated exposure = target use exposure / AF

AF greater than one means the modeled test condition consumes life faster. Equivalent exposure is valid only for the same mechanism and model parameters.

Arrhenius temperature model

AF = exp[(Ea / k) × (1 / Tuse − 1 / Ttest)]

T is absolute temperature in kelvin, Ea is activation energy in electron volts, and k is 8.617333262 × 10−5 eV/K. The test temperature must exceed the use temperature. Calculator.

Inverse power law

Life = A × S−n; AF = (Stest / Suse)n

S is one positive stress measure in a consistent unit and n is a positive stress-life exponent. The relationship must be supported over the selected range. Calculator.

Combined temperature-humidity model

AF = exp[(Ea / k) × (1 / Tuse − 1 / Ttest)] × (RHtest / RHuse)γ

RH values are relative humidities used in the same percent or fractional convention, and γ is the fitted humidity exponent. Both accelerated conditions exceed their use values in this tool. Calculator.

Reduced Coffin-Manson temperature-range model

AF = (ΔTtest / ΔTuse)m

ΔT is the cycle temperature range in the same temperature-difference unit and m is a positive exponent. This reduced form omits frequency and maximum-temperature terms present in modified models. Calculator.

Parameter and model boundaries

Activation energy and exponents are fitted or mechanism-specific inputs, not universal defaults. Temperature, humidity, voltage, load, frequency, and other stresses can interact. Reject any extrapolation that crosses a mechanism transition, material limit, condensation regime, threshold, yielding condition, or electrical breakdown.

Scope and source

These formulas return deterministic point factors. They do not estimate parameter uncertainty, fit a life distribution, calculate confidence bounds, determine sample size, or prove qualification. Technical basis: NIST Engineering Statistics Handbook sections on acceleration model selection, Arrhenius acceleration, and inverse-power and combined models. See the model-selection guide for workflow.