Weibull B10 Life (β, η)
Turn a Weibull shape and characteristic life into B10 (or any B-life), median life, and MTTF — the numbers a warranty or bearing spec actually asks for.
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The engineering
A B-life is the time by which a stated fraction of the population has failed: B10 means 10% failed, 90% surviving. Given the two Weibull parameters — shape β (how failures cluster in time) and characteristic life η (the time by which 63.2% have failed, regardless of β) — this card inverts the Weibull CDF to get any B-life, plus the median (B50) and the mean life MTTF via the gamma function. B10 is the lingua franca of bearing catalogs (where it's called L10) and increasingly of motor, fan, and electrolytic-capacitor specs.
Sanity checks: at any β, the B63.2 life equals η exactly. For β = 1 the Weibull collapses to the exponential and MTTF = η. And don't quote MTTF for a wear-out mode (β > 1) as if it were a constant failure rate — an MTTF of 886 hours with β = 2 means almost nothing fails early and nearly everything fails in a band around the mean, which is a completely different maintenance picture than an exponential with the same MTTF.
Where this math comes from
The B10 idea predates the distribution: Arvid Palmgren at SKF was rating ball bearings by the life 90% of a batch would survive back in 1924, because bearing scatter made a single 'the life' number meaningless. Waloddi Weibull — a Swedish military engineer working on strength of materials and bearing steels — proposed his flexible two-parameter distribution in 1939 and made the famous case for it in his 1951 ASME paper, showing one function could fit everything from yield strength of steel to the height of British men.
American reliability engineering initially resisted, wedded to the exponential distribution. Robert Abernethy — a Pratt & Whitney engineer who used Weibull analysis on jet-engine failures — spent decades making it the industrial standard, and his self-published New Weibull Handbook remains the working reference for β-η analysis, B-lives, and the small-sample rank-regression methods that feed calculators like this one.
- 1924Arvid Palmgren (SKF)Rates bearings by 90%-survival life — the original B10/L10.
- 1939Waloddi WeibullProposes the distribution in a Swedish engineering academy paper on material strength.
- 1951Waloddi WeibullASME paper 'A Statistical Distribution Function of Wide Applicability' makes the case with seven datasets.
- 1993Robert B. AbernethyPublishes The New Weibull Handbook, the practitioner's standard for β-η analysis.
- 2007ISOISO 281 pins the L10 basic rating life for rolling bearings on Weibull statistics.
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