Why can I test fewer units for longer?

Because under a Weibull model with β > 1, running past the required life accumulates more damage per unit. Extending test time to twice the required life with β = 2 cuts the required sample size roughly fourfold. This only works if beta is known from prior data — assuming a favourable beta to shrink the sample is how demonstrations become fiction.

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Reliability Test Sample Size Calculator

A reliability demonstration test answers: how many units must survive the test, with no failures, before I can claim reliability R at confidence C? The success-run formula gives the answer directly, and its results are often uncomfortably large — which is exactly the point.

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Formula

Zero-failure sample sizen = ln(1 − C) / ln(R)

Demonstrated reliability from n survivorsR = (1 − C)^(1/n)

With allowed failures (chi-square)T = [ χ²(α, 2r+2) / 2 ] × MTBF_required

T is total test time, r is number of allowed failures.

Weibull test-time trade-offn = ln(1 − C) / [ (t_test / η)^β · (−1) ]

Testing longer than the required life reduces the sample size needed.

Worked example

Demonstrate 95% reliability at 90% confidence with zero failures.

n = ln(1 − 0.90) / ln(0.95)
ln(0.10) = −2.302585; ln(0.95) = −0.0512933
n = 44.89 → round up to 45
Raising the target to 99% reliability: n = ln(0.10)/ln(0.99) = 229.1 → 230

45 units must survive the full test duration with no failures. Note the cost of the reliability target: moving from 95% to 99% multiplies the sample by more than five. When 230 units is unaffordable, the usual escape is to test fewer units for longer than the required life and use the Weibull relationship — but that requires knowing beta.

Run this with your own numbers

Common mistakes

Running the test for less than the required life and still claiming reliability at that life. Test duration and the reliability claim must refer to the same time.
Treating a failure as an outlier and continuing. One failure invalidates the zero-failure assumption; requantify with the chi-square form.
Confusing confidence with reliability. 90% confidence in 95% reliability is not 95% confidence in 90% reliability.
Assuming an exponential distribution to reduce sample size for a component that clearly wears out.

Frequently asked questions

Why can I test fewer units for longer?: Because under a Weibull model with β > 1, running past the required life accumulates more damage per unit. Extending test time to twice the required life with β = 2 cuts the required sample size roughly fourfold. This only works if beta is known from prior data — assuming a favourable beta to shrink the sample is how demonstrations become fiction.

About Reliability Pro

Sample Size 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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