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Reliability Growth Calculator (Crow-AMSAA)

Reliability growth models track whether a test-analyse-and-fix programme is actually improving the product. The Crow-AMSAA (NHPP power law) model fits cumulative failures against cumulative time; the growth parameter β tells you whether reliability is improving, flat, or getting worse.

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Formula

Cumulative failuresN(t) = λ · t^β
Cumulative MTBFMTBF_cum = t / N(t) = t^(1−β) / λ
Instantaneous MTBFMTBF_inst = 1 / (λ · β · t^(β−1))
RelationshipMTBF_inst = MTBF_cum / (1 − β)
Valid for β < 1.

Worked example

A development programme fits λ = 0.45 and β = 0.65 over 2000 cumulative test hours.

  1. N(2000) = 0.45 × 2000^0.65 = 0.45 × 139.85 = 62.9 failures
  2. MTBF_cum = 2000 / 62.9 = 31.8 hours
  3. MTBF_inst = 31.8 / (1 − 0.65) = 31.8 / 0.35 = 90.8 hours
  4. To reach 150 h instantaneous MTBF: t = [1 / (150 × λ × β)]^(1/(β−1)) ≈ 49,200 cumulative hours.

Cumulative MTBF is 31.8 hours but current (instantaneous) MTBF is 90.8 hours — the cumulative figure is dragged down by early failures already fixed. Report the instantaneous value as the current capability and the cumulative value only as history. The second observation is harsher: reaching 150 h at this growth rate needs roughly 49,200 cumulative test hours, about 25 times the testing done so far. Growth models are as useful for showing a target is unreachable as for showing progress.

Run this with your own numbers

How to interpret the result

β < 1Reliability is growing — time between failures is increasing.
β = 1Homogeneous Poisson process. No growth; failure rate is constant.
β > 1Reliability is deteriorating — failures are getting more frequent.

Common mistakes

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Reliability Growth 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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