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.
Formula
Worked example
A development programme fits λ = 0.45 and β = 0.65 over 2000 cumulative test hours.
- N(2000) = 0.45 × 2000^0.65 = 0.45 × 139.85 = 62.9 failures
- MTBF_cum = 2000 / 62.9 = 31.8 hours
- MTBF_inst = 31.8 / (1 − 0.65) = 31.8 / 0.35 = 90.8 hours
- 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.
How to interpret the result
| β < 1 | Reliability is growing — time between failures is increasing. |
| β = 1 | Homogeneous Poisson process. No growth; failure rate is constant. |
| β > 1 | Reliability is deteriorating — failures are getting more frequent. |
Common mistakes
- Reporting cumulative MTBF as current reliability. It always lags the true present state during growth.
- Fitting the model when corrective actions were not actually implemented — growth models assume fixes are effective and incorporated.
- Extrapolating growth indefinitely. Growth flattens as design-limited failure modes come to dominate.
- Mixing failures from different configurations without resetting the analysis at major design changes.
Related tools
About Reliability Pro
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.