How to run a Weibull analysis
Weibull.Genie is a reliability workbook for hardware life data. You enter times and F/S, fit a two-parameter Weibull model, then reuse those parameters for B-lives, MTTF, hazard, fleet risk, accelerated life, and demonstration tests. It is not a PDF/CDF sketching toy, and it is not a certified life assessment.
Open the Weibull.Genie workbook Open Weibull Calculator
The 2P Weibull model
Unreliability (the CDF) and reliability are
F(t) = 1 − exp[−(t/η)β]
R(t) = exp[−(t/η)β]
Characteristic life η is the scale: 63.2% of units have failed by t = η, for any β. Mean life (MTTF) is η Γ(1 + 1/β) and equals η only when β = 1. Shape β sets the hazard trend — falling, flat, or wear-out — which is why reliability engineers estimate both parameters from data instead of drawing a CDF by eye.
How to do it in the workbook
- Open the Weibull Workbook. Enter time, F (failed) or S (suspended), and quantity. Optional STRESS is for ALT, not for a single-stress endurance set.
- Leave Distribution model on Arrhenius-Weibull unless you have a temperature or voltage acceleration story. Fit method MLE is the default.
- Read β and η, then check the probability plot. Points should track the fitted line; a 95% Fisher band is available when the grid has no numeric STRESS.
- On Weibull Calculator, evaluate R(t), B10, MTTF, or h(t) from the same LifeFit. Mission / fleet risk and RDT live on their own tabs.
- Export Excel or PowerPoint if you need a record. Recalculate after edits — the workbook is client-side and does not silently keep a stale fit.
Worked example: spindle bearings (right-censored)
The built-in bearing sample is 12 failures and 7 suspensions (quantity on the S rows). Times in hours: failures at 167, 223, 284, 318, 376, 419, 468, 512, 571, 640, 718, 805; two suspensions at 450, two at 600, three at 850.
Weibull.Genie MLE on that set is β ≈ 2.168 and η ≈ 716.2 h. β > 1 is wear-out, as expected for bearings. From those two numbers:
| Quantity | Formula | Value |
|---|---|---|
| B10 life | η [−ln(0.9)]1/β | 254 h |
| B50 (median) | η [−ln(0.5)]1/β | 605 h |
| Characteristic life | η at F ≈ 63.2% | 716 h |
| MTTF | η Γ(1 + 1/β) | 634 h |
| R(500 h) | exp[−(500/η)β] | 0.632 |
Load bearing sample on the workbook to reproduce the fit, then open Weibull Calculator for B10 / MTTF / hazard with the same LifeFit. For the closed-form identities with round numbers, see the B10, MTTF, and hazard rate pages (β = 2, η = 1 000 h).
FAQ
What is two-parameter Weibull analysis?
It fits a shape β and a characteristic life η to failure and suspension times. The CDF is F(t) = 1 − exp[−(t/η)^β]. Reliability is R(t) = 1 − F(t). η is the 63.2% failed life, not the mean.
How should right-censored units be entered?
Mark failures as F and survivors as S (suspensions) at the time they were last seen unfailed. Quantity can repeat identical rows. Maximum-likelihood estimation lets failures contribute the density f(t) and suspensions contribute R(t).
What does β tell you?
β < 1 is a falling hazard (infant mortality). β ≈ 1 is roughly constant hazard (exponential / useful life). β > 1 is a rising hazard (wear-out). A wide interval on β means the shape is poorly identified — add failures or test longer.
Is Weibull.Genie a PDF/CDF curve sketching tool?
No. It is a reliability workbook: life-data grid, 2P Weibull or lognormal fit, Arrhenius / IPL accelerated life, reliability demonstration (RDT), fleet risk, and Excel / PowerPoint export. Plotting F(t) is a result of the fit, not the product.