What does the Weibull shape parameter β tell me?

β describes how the failure rate changes with time. β 1 means an increasing hazard (wear-out). Identifying β tells you which part of the bathtub curve you are in and what corrective action makes sense.

What is the characteristic life η?

η (eta) is the scale parameter — the age by which 63.2% of the population has failed, regardless of β. It sets the time axis of the distribution. Two designs with the same η but different β have very different early-life behaviour.

What is B10 (or L10) life?

The B10 (bearings call it L10) life is the time by which 10% of the population is expected to have failed — a common reliability rating. It is η·(−ln 0.9)^(1/β), and for many components is a more useful design target than the mean life.

Reliability · guide

Weibull analysis of life data

The Weibull distribution is the workhorse of reliability engineering because one flexible form can describe infant mortality, random failures, and wear-out. Fit it to failure data and you get the failure mode, the design life, and the warranty exposure in a few parameters.

One distribution, three behaviours

The two-parameter Weibull cumulative failure probability is:

F(t) = 1 − exp[ −( t / η )^β ]

with β the shape parameter and η the characteristic life. The power of the form is that β alone selects the failure regime:

β < 1 — decreasing hazard: infant mortality (defects, bad assembly). Burn-in helps.
β = 1 — constant hazard: random failures (the exponential distribution). Redundancy helps.
β > 1 — increasing hazard: wear-out (fatigue, corrosion, erosion). Scheduled replacement helps.

That mapping is why a Weibull fit is diagnostic, not just descriptive — β points at the physical failure mechanism and the right intervention.

The numbers you report

From a fitted (β, η) the common reliability metrics follow directly:

B10 life = η · ( −ln 0.9 )^(1/β)

MTTF = η · Γ( 1 + 1/β )

where Γ is the gamma function. Note that the mean (MTTF) and the characteristic life η coincide only when β = 1; for wear-out distributions they differ, so quoting the mean alone can mislead.

Reading a Weibull plot

Taking the double logarithm linearises the CDF, so failure data plotted on Weibull axes fall on a straight line whose slope is β and whose position gives η. Curvature or a "dog-leg" is a signal that more than one failure mode is present and the data should be split before fitting.

Open the calculatorWeibull reliability calculator →Fit β and η to failure/censored data, get B10 and MTTF with confidence bounds, and see the Weibull probability plot and hazard curve.

Practical cautions

Handle censored data properly (units that have not yet failed carry information), be honest about small-sample uncertainty (confidence bounds on β and η widen quickly with few failures), and split mixed failure modes rather than forcing one line through them. A clean Weibull fit on the wrong, pooled data is worse than no fit.

Frequently asked

What does the Weibull shape parameter β tell me?: β describes how the failure rate changes with time. β < 1 means a decreasing hazard (infant mortality / early-life defects), β = 1 means a constant hazard (random failures, the exponential case), and β > 1 means an increasing hazard (wear-out). Identifying β tells you which part of the bathtub curve you are in and what corrective action makes sense.
What is the characteristic life η?: η (eta) is the scale parameter — the age by which 63.2% of the population has failed, regardless of β. It sets the time axis of the distribution. Two designs with the same η but different β have very different early-life behaviour.
What is B10 (or L10) life?: The B10 (bearings call it L10) life is the time by which 10% of the population is expected to have failed — a common reliability rating. It is η·(−ln 0.9)^(1/β), and for many components is a more useful design target than the mean life.

References

W. Weibull, "A Statistical Distribution Function of Wide Applicability," J. Applied Mechanics, 1951.
R.B. Abernethy, "The New Weibull Handbook."
ReliaSoft, "Life Data Analysis Reference."
IEC 61649, "Weibull analysis."

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