Weibull Reliability Estimate Calculator

Work out weibull reliability estimate instantly with clear inputs, formula shown and shareable results.

About Weibull Reliability Estimate Calculator

The two-parameter Weibull distribution gives R(t) = exp(-(t/eta)^beta). Beta below 1 indicates infant mortality, beta near 1 random failure and beta above 1 wear-out. The B-life at a target reliability is eta x (-ln R)^(1/beta), and mean life is eta x gamma(1 + 1/beta).

Formulas

Weibull reliability

R(t) = exp(-(t / eta)^beta)

Hazard and B-life

h(t) = (beta / eta) x (t / eta)^(beta-1); B-life = eta x (-ln R)^(1/beta)

Worked example

With the default values below, Weibull Reliability Estimate Calculator returns Reliability At Time of 80.4417%. Change any input above and every figure here is recalculated in your browser.

Inputs used

Shape Parameter (beta)minimum 0.05: 2.2
Scale Parameter (eta)minimum 0.01 hours: 8,000 hours
Time Of Interestminimum 0.01 hours: 4,000 hours
Target Reliabilityaccepts 0.1–99.99 %: 90 %

Results

Reliability At Time: 80.4417%
Instantaneous Hazard Rate: 0.00011970
Life At Target Reliability: 2,876.42
Mean Life: 7,085.00

Step by step

1Values used
2Weibull reliability
3Hazard and B-life
4Reliability At Time= 80.4417
5Instantaneous Hazard Rate= 0.00011970
6Life At Target Reliability= 2,876.42
7Mean Life= 7,085.00

Assumptions and limits

The result is derived only from the 4 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to 8 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

What does the shape parameter tell me about the failure mechanism?

Beta near 0.5 points to manufacturing defects or installation error, beta 1 to random external causes, beta 2-4 to fatigue and abrasion, and beta above 5 to rapid wear-out or corrosion end-of-life.

How are beta and eta obtained?

By fitting failure data on a Weibull probability plot, or by maximum likelihood estimation. Suspended items that have not yet failed must be included as censored data or beta will be badly overstated.