QM Bench

Weibull analysis: theory, B10 life and a reliability case study

What the Weibull shape and scale parameters mean, how to read a Weibull plot, how B10 life and MTTF are calculated and a worked life-test example.

Ľubomír Blažek
Automotive quality manager · updated 2026-10-25

Try it while you read

Open the free Weibull Analysis tool and click Load sample: it reproduces the case study below.

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Theory: one distribution, three failure modes

The Weibull distribution describes time to failure very flexibly with two parameters: the shape β and the scale η.

R(t) = exp(−(t / η)^β)    B10 = η · (−ln 0.9)^(1/β)    MTTF = η · Γ(1 + 1/β)
  • β < 1: failure rate decreases, early failures from manufacturing defects.
  • β ≈ 1: constant failure rate, random failures.
  • β > 1: failure rate increases, wear-out (fatigue, abrasion, corrosion).

η is the characteristic life: 63.2 % of the units have failed by then, whatever β is. On a Weibull plot (ln t against ln(−ln(1 − F))) the data form a straight line with slope β.

Key point

β decides the maintenance strategy: only for wear-out (β > 1) does preventive replacement reduce failures.

Step by step

  1. Collect the times to failure from a test or field data.
  2. Paste them and choose the unit.
  3. Check the plot: points close to the line mean the model fits.
  4. Read β, η, B10 and MTTF; enter the mission time for its reliability.

Case study: life test of 8 actuators

Eight actuators are run to failure on a test bench: 120, 190, 240, 310, 365, 420, 500 and 610 hours (the Load sample data).

  • β = 2.45: wear-out.
  • η = 390 hours, MTTF 345 hours.
  • B10 = 155 hours, B1 = 59 hours.
  • Reliability at the 200-hour mission: 82 %.

The customer requires B10 ≥ 300 hours, so the design fails the requirement. Because the failures are wear-out, the team looks at the bearing material and lubrication rather than at assembly quality.

Common mistakes

  • Mixing failure modes (early and wear-out) in one fit: the plot bends.
  • Ignoring units that did not fail; a censored analysis is needed for those.
  • Drawing conclusions from 3 or 4 failures.

Frequently asked questions

Is MTTF the same as MTBF?

For non-repairable items the mean life is MTTF. MTBF is used for repairable systems. For a Weibull with β = 1 (exponential) both equal η.