Skip to content

Free calculator, no sign-up

Weibull analysis: reliability, hazard rate and MTBF

Fit β and η to your times to failure by median rank regression, then read reliability R(t), hazard rate, MTBF and replacement age. Free, no sign-up.

  • Instant result
  • Formula and standards shown
  • On desktop and phone

Pre-filled example

A wear-out component (β = 2, η = 1,000 h): its reliability over a 500-hour mission, and the time after which only a 90% chance remains that it has not failed.

h
h
h
%

Result

886.23hMTBF

Reliability R(t)
0.7788
Hazard rate λ(t)
0.001000/h
Time for target reliability
324.59 h
Attach this calculation to a work order

Free during the beta, no credit card

A Weibull fit kept with the component's history

Here, the calculator is free and the result is gone when you close the page. In Reglova, it is attached to the work order on the right machine: you find it again at the next breakdown, and on audit day.

The CMMS software comparison, our gaps included
  • Attached to the work order with its inputs: the server recalculates it, it stays verifiable.
  • On the technician's phone, even without a network.
  • In the machine's history, for the next breakdown.
Try the demoJoin the free beta
Reglova · Calculations · Work order WO-AT01-04219
Silent video, 33 s: from the work order for an oil leak on a shear cylinder, the tightening torque of an M12 bolt, then "Attach to the work order". A step to tighten it to 93.1 N·m lands in the checklist (step text from the French demo data). Watch the video

When a Weibull analysis pays off

  1. 01

    Find out whether a component wears out (β > 1), and so whether preventive replacement makes sense.

  2. 02

    Set a replacement interval for a target reliability, for example 90%.

  3. 03

    Estimate the probability of completing a given mission time.

Good to know

With fewer than six times, the fit is unreliable: the calculator says so. Tests stopped without a failure (censored data) are not taken into account.

Weibull reliability function and median rank regression

The Weibull distribution describes a component's life with two parameters: the shape β, which tells whether failures are early, random or wear-out, and the scale η. Enter them, or paste your times to failure: the calculator fits them by median rank regression (Bernard's approximation).

Formula · Reference documents

R(t) = exp[−((t − γ)/η)^β] ; λ(t) = (β/η)·((t − γ)/η)^(β−1) ; MTBF = γ + η·Γ(1 + 1/β) ; t(R) = γ + η·(−ln R)^(1/β) ; Bernard: Fi = (i − 0.3)/(N + 0.4)

ReliaWiki (median rank regression) ; ISO 14224

Inputs and accepted ranges
InputUnitAccepted rangeExample
Data2 optionsParameters β and η
Shape βif Data: Parameters β and η0.1 to 102
Scale ηif Data: Parameters β and ηh0.001 to 1,000,000,0001,000 h
Location γh0 to 1,000,000,0000 h
Times to failureif Data: Recorded timesh3 to 1,000
Mission time th0 to 1,000,000,000500 h
Target reliability%0.01 to 99.9990 %
Calculated results
  • MTBFh
  • Shape β
  • Scale ηh
  • Coefficient r²
  • Reliability R(t)
  • Hazard rate λ(t)/h
  • Time for target reliabilityh
What the calculator flags
  • Fewer than six times: the fit is uncertain.
  • Suspended items are not taken into account.

Every breakdown dated in the machine history

  • Breakdowns reported by QR code
  • Work orders on the phone, even without a network
  • Mandatory inspections reminded by email
  • Audit file as a PDF, in one click
Try the demoJoin the free beta

Free during the beta, no credit card