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Inverse Power Law Calculator

The inverse power law models life under a non-thermal stress — voltage, vibration level, pressure, mechanical load. Life falls as a power of the stress ratio, so the exponent n does all the work: small changes in n produce large changes in the claimed field life.

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Formula

Life at stress SL(S) = A · S^(−n)
Acceleration factorAF = (S_stress / S_use)^n
Vibration (Grms) formAF = (G_test / G_field)^m
m ≈ 4 is a common default for random vibration fatigue.
Combined with ArrheniusAF_total = AF_temperature × AF_stress

Worked example

A capacitor is tested at 450 V against a use condition of 300 V, with a voltage exponent n = 3.

  1. Stress ratio = 450 / 300 = 1.5
  2. AF = 1.5³ = 3.375
  3. 1000 test hours ≈ 3375 field hours
  4. If n were 5 instead: AF = 1.5⁵ = 7.59, more than double the claim.

The acceleration factor is 3.375, so 1000 test hours represent about 3,375 field hours. The n = 3 versus n = 5 comparison is the important part: the exponent must come from multi-stress-level testing, not from a handbook, if the resulting life claim is going to survive scrutiny.

Run this with your own numbers

Common mistakes

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Power Law Model is part of a suite of 126 reliability, maintenance and quality engineering tools covering life data analysis, accelerated testing, system reliability, FMEA and root cause, SPC, and design for reliability. It runs in the browser and as native iOS and Android apps, so the same calculation is available at a desk or in front of the asset.

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