What is Weibull analysis?
Weibull analysis is the most widely used method in life data analysis. The Weibull distribution, introduced by Waloddi Weibull in 1951, can describe falling, constant and rising failure rates with one formula, so it fits the life of everything from electronic components to bearings and seals. On a Weibull plot, data that follows the distribution lies on a straight line whose slope is β.
What β tells you
| β | Failure pattern | Typical causes | Maintenance |
|---|---|---|---|
| < 1 | Early failures, falling rate | Manufacturing defects, poor installation | Burn-in, better quality and installation; replacing early makes it worse |
| ≈ 1 | Random, constant rate | External events, overloads, mixed modes | Condition monitoring or redundancy |
| 1 to 4 | Wear-out | Fatigue, wear, corrosion | Planned replacement or condition monitoring before B10 |
| > 4 | Rapid wear-out | Old age, design limit reached | Scheduled replacement works well |
Weibull analysis example
Twelve conveyor drive bearings were run on a test rig: nine failed between 1,150 and 3,900 hours, and three were still running at 2,000, 3,000 and 4,000 hours. Rank regression gives β = 2.75 and η = 3,268 h, with points close to the line (R² 0.999). β above 1 confirms wear-out. The B10 life is 1,443 h, the mean life 2,908 h, and the reliability over the first 1,000 h is 96.2%. Maximum likelihood gives a similar fit (β 3.19, η 3,208 h). The plant sets bearing replacement or vibration checks well before 1,400 hours.
Tips
- One failure mode at a time. Mixing modes with different β gives a bent plot and a misleading fit; separate them first.
- Always include suspensions.
- Use the right age: operating hours or cycles, not calendar time, if usage varies.
- For life at use conditions from tests at higher stress, see accelerated life testing; to decide what maintenance to do, use RCM.
How to use this Weibull Analysis tool
- Enter the data. Enter or paste each unit's time: F for failures, S for suspensions (units that have not failed).
- Choose the method. Use rank regression for small samples and to check the fit on the plot, or maximum likelihood for heavily censored data.
- Set a mission time. Optionally enter an age to get the reliability at that age.
- Read the parameters. β tells you the failure pattern, η the characteristic life; B10 and mean life follow.
- Check the plot. Points should lie close to the line. A curve or a dog-leg suggests mixed failure modes or a failure-free period.
- Export. Export the plot, parameters and median ranks to PDF, PNG or Excel.
Frequently asked questions
What is Weibull analysis?
Weibull analysis fits a Weibull distribution to times to failure (hours, cycles, kilometres) to describe how an item fails over its life. Its shape parameter β tells you whether failures are early, random or wear-out, and its scale parameter η is the characteristic life. From the fit you get the reliability at any age, B10 life and mean life.
What do β and η mean?
β (shape) below 1 means a falling failure rate (infant mortality), about 1 a constant rate (random failures) and above 1 a rising rate (wear-out). η (scale, characteristic life) is the age by which 63.2% of units have failed, whatever β is.
What is a suspension?
A unit that has not failed: still running at the end of the test or in the field, or removed for another reason. Suspensions carry information (the unit survived that long) and must be included; leaving them out makes the life look shorter than it is.
Rank regression or maximum likelihood?
Rank regression fits a straight line on the Weibull plot using median ranks, and is the traditional method for small samples (up to about 20 failures) because it is easy to see and check. Maximum likelihood uses the exact times and handles heavy censoring better with larger samples. When the two disagree a lot, the data may mix failure modes.
What is B10 life?
The age by which 10% of units are expected to fail (90% reliability). It is widely used for bearings and other wear-out parts, and is often a better maintenance interval guide than the mean life. B1 is the age at 1% failed.
How many failures do I need?
You can fit with two, but estimates are very uncertain below about 5 to 6 failures. With few failures, use β from experience with similar parts (Weibayes) and treat results as indicative.