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Weibull Reliability and B10 Life Calculator

Weibull analysis is the standard way to describe life data. If you already have a shape and scale from your data, this calculator gives reliability, B-life and hazard rate in seconds.

Your numbers

Shape parameter (beta)

Below 1 is infant mortality, near 1 is random failure, above 1 is wear-out.

Scale parameter (eta)

hours

Characteristic life: time by which 63.2% of units have failed.

Mission time

hours

B-life failure percentage

Your results

Reliability at mission time

97.1%

B-life (time to selected failure percentage)

3,595.53

In the same unit as eta.

Probability of failure by mission time

2.9%

Hazard rate at mission time (per hour)

Failure regime (1 = wear-out, 0 = not)

Two-parameter Weibull with no failure-free period. Parameters should come from a fitted life data set with stated confidence.

Save results:

Reliability (%) vs mission time

Sweeps Mission time from 100 to 20000, holding your other inputs fixed.

Life data from maintenance records

Optional review of assembling run hours and failures from your ERP maintenance module.

Optional. The tool and every export work without this. No spam.

How to use the calculator

Enter beta and eta from your fitted data, then a mission time in the same unit as eta. Choose which B-life you need; B10 is the time by which 10 percent of units are expected to fail and is common for bearings and rated components. The chart sweeps mission time to show how reliability decays and where it crosses your requirement.

The formulas

Reliability is R(t) = exp(-(t/eta)^beta). The B-life for failure fraction F is t = eta times (-ln(1-F))^(1/beta). The hazard rate is h(t) = (beta/eta)(t/eta)^(beta-1). When beta equals 1 the model reduces to the exponential distribution with constant hazard. At t = eta, reliability is about 36.8 percent regardless of beta.

Beta below 1: failure rate falls with time (infant mortality).
Beta near 1: random failures, age does not matter.
Beta above 1: wear-out, preventive replacement can pay off.

Linking to FMEA occurrence

A failure probability at a mission time supports an occurrence rating for a DFMEA cause. State the mission profile and confidence in the rating justification. For a repairable system, Weibull on first failures differs from system-level rates, so keep the data set consistent with the question you are asking.

Common mistakes

Fitting a Weibull to too few failures gives wide confidence bands, so the single-point answer here may look far more precise than it is. Mixing failure modes in one data set often produces a beta near 1 that hides a wear-out mode. Also remember to treat suspended (still running) units correctly when fitting.

Frequently Asked Questions

What does B10 mean?

B10 life is the time by which 10 percent of a population is expected to fail, so 90 percent are still working. It is widely used for bearings and rated mechanical parts.

What if beta is exactly 1?

The distribution becomes exponential with constant failure rate 1/eta. Reliability then equals exp(-t/eta) and MTBF equals eta.

Can I use cycles or miles instead of hours?

Yes. Use one unit consistently for eta and mission time. The hazard output will then be per that unit.

How do I get beta and eta?

Fit them from failure and suspension data using median rank regression or maximum likelihood in a statistics tool, then enter the fitted values here.

Netray can pull run hours and failure events from maintenance and quality records in your ERP to build the life data set for this analysis.

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