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B10 life: definition, formula, and a worked example

B10 life is the time by which 10% of a population is expected to have failed — equivalently, the time each individual unit survives with 90% probability. It's the 10th percentile of the life distribution:

F(B10) = 0.10

The "B" convention generalises: B1 is the 1% point, B50 the median. Bearing engineers know the same quantity as L10 — the two are identical; "L" (life) is simply the bearing industry's letter, from the rating-life standards where the concept was born.

The Weibull formula

Invert the Weibull CDF, F(t) = 1 − exp(−(t/η)^β), at F = 0.10:

B10 = η · (−ln 0.9)^(1/β)  =  η · (0.10536)^(1/β)

and in general, for any fraction q:

Bq = η · (−ln(1 − q))^(1/β)

Worked example

A fitted Weibull for a population of conveyor bearings: η = 6,000 hours, β = 2.5 (wear-out).

B10 = 6000 × (0.10536)^(1/2.5)
    = 6000 × (0.10536)^0.4
    = 6000 × 0.4065
    ≈ 2,439 hours

For contrast, from the same model: the median (B50) is ≈ 5,182 hours and the mean (MTTF) is ≈ 5,324 hours. Read those three numbers together: by the "average life" of 5,324 hours, roughly half the fleet is already dead. The B10 at 2,439 hours is the number that tells you when failures start arriving in earnest — which is what a maintenance planner actually needs to know. (More on that gap in MTBF vs MTTF.)

The shape parameter matters enormously here. With the same η = 6,000 but β = 1 (random failures), B10 = 6000 × 0.10536 ≈ 632 hours — early failures arrive four times sooner despite the identical characteristic life. A mean can't see this difference; a B-life is built from it.

Why B-lives beat means for decisions

They answer the real question. "When do failures start?" is a percentile question. The mean answers "where's the balance point of the distribution?", which no maintenance decision actually hinges on.
They map to risk targets. "No more than 10% failure probability before overhaul" translates directly to "interval ≤ B10". Warranty and safety cases work the same way with B1 or B0.1.
They come with uncertainty. Fitted from data by maximum likelihood, a B10 carries confidence bounds. Eight failures might give you B10 ≈ 494 h with bounds wide enough to change the decision — better to know that than to discover it in the field.

One caution: a B10 is only as good as the fit behind it. It's an extrapolation into the lower tail of the distribution, exactly where data is thinnest — so the fit must use all the evidence, especially the suspensions (here's why that matters), and ideally more than a handful of failures.

Frequently asked questions

What's the difference between B10 and L10?

None — they're the same 10th-percentile life. L10 is the bearing industry's notation (from rating-life standards such as ISO 281); B10 is the general reliability-engineering term, reputedly from the German Brucheinleitzeit era of bearing testing. Use whichever your audience expects.

How is B10 related to reliability?

Directly: R(B10) = 0.90. A unit reaching its B10 age has a 90% chance of having survived. In general R(Bq) = 1 − q/100 for a Bq life.

Can B10 be longer than the MTBF?

For non-repairable items compare against MTTF: B10 is essentially always shorter than the mean (it would take an extremely steep wear-out, β above roughly 22, for 10% of failures to arrive later than the mean). If someone quotes you a B10 above the mean life, one of the two numbers is wrong.

What sample size do I need to estimate B10?

There's no magic minimum, but since B10 lives in the tail, small samples give wide bounds. As a rule of thumb, with fewer than ~10 failures expect the B10's confidence interval to span a factor of two or more — fit with maximum likelihood, report the bounds, and let them inform how conservative the interval should be.