Weibull analysis: β, η and B10 life from failure-time data
Paste your failure times and mark suspended (censored) records with S. See the shape and scale parameters, B10 life, reliability at a given time and the maintenance interval for a target reliability. The calculation runs in your browser.
One record per line. Add S to records that were removed without failing or are still running (censored), for example 1250 S. You can paste a column from Excel.
13 records · 10 failures · 3 censored
Evaluation
- Shape parameter β
- Rank regression (RRX): 2.942MLE3.49
- Scale parameter η
- Rank regression (RRX): 1,118 hoursMLE1,098 hours
- B10 life
- Rank regression (RRX): 520.2 hoursMLE576.1 hours
Results
| Measure | Rank regression (RRX) | Maximum likelihood (MLE) |
|---|---|---|
| Shape parameter β | 2.942 | 3.49 |
| Scale parameter η | 1,118 hours | 1,098 hours |
| R² (fit to line) | 0.9994 | — |
| B1 life | 234 hours | 293.8 hours |
| B10 life | 520.2 hours | 576.1 hours |
| B50 life (median) | 987 hours | 988.4 hours |
| Mean life (MTTF) | 997.4 hours | 987.7 hours |
| Reliability R(t), t = 500 hours | 91% | 93.8% |
| Conditional reliability (500 → +500 hours) | 53.4% | 51.8% |
| Maintenance interval (R = 90%) | 520.2 hours | 576.1 hours |
Failure pattern
1.1 < β ≤ 4: wear-out failures; the failure rate rises with age. Preventive replacement or planned maintenance makes sense, and the maintenance interval below is a useful guide.
If the points on the probability plot do not follow the line but form a curve or a kink, several failure modes may be mixed; if R² is low, treat the results with caution.
If RRX and MLE differ a lot (especially in small samples with few failures), treat both results as a range rather than exact values.
- Failure points
- RRX line
- MLE line
Show rank table
| Rank | Time | Status | Adjusted rank | F (median rank) |
|---|---|---|---|---|
| 1 | 410 | Failure | 1 | 5.2% |
| 2 | 560 | Failure | 2 | 12.7% |
| 3 | 620 | Censored | — | — |
| 4 | 690 | Failure | 3.09 | 20.8% |
| 5 | 780 | Failure | 4.18 | 29% |
| 6 | 870 | Failure | 5.27 | 37.1% |
| 7 | 900 | Censored | — | — |
| 8 | 960 | Failure | 6.52 | 46.4% |
| 9 | 1,050 | Failure | 7.77 | 55.7% |
| 10 | 1,100 | Censored | — | — |
| 11 | 1,160 | Failure | 9.32 | 67.3% |
| 12 | 1,290 | Failure | 10.88 | 79% |
| 13 | 1,480 | Failure | 12.44 | 90.6% |
F = (adjusted rank − 0.3) / (n + 0.4) · R(t) = exp(−(t/η)^β) · Bp = η · (−ln(1−p))^(1/β) · MTTF = η · Γ(1 + 1/β)
Data is processed in your browser and is not sent anywhere.
This analysis is a preliminary assessment. Few failures, mixed failure modes or incorrect censoring can distort it badly; confidence bounds are not shown. Review data quality and failure modes with an expert before making decisions.
Would you like to combine the Weibull result with your SCADA and sensor data to see which equipment needs attention, and when?
Request a call01
How to use it
A
Paste failure times line by line (hours, cycles or km); add S to records that are still running or were removed without failing.
B
Choose the unit; optionally enter the time t at which you want the reliability, the current age and the target reliability.
C
Review β and η, B10 life and the probability plot; if RRX and MLE are close, the estimate is more trustworthy.
02
What does a Weibull analysis tell you?
The Weibull distribution describes life with two parameters. The shape parameter β tells how the failure rate changes with time: β < 1 means it decreases (early-life failures), β ≈ 1 constant (random failures), β > 1 increasing (wear-out). The scale parameter η (characteristic life) is the time by which about 63.2% of units have failed.
B10 life is the time by which 10% of units are expected to fail, in other words the 90% reliability time. For parts such as bearings, life ratings are usually given as B10. B1 is more conservative and B50 is the median life; mean life (MTTF) is η·Γ(1 + 1/β) and differs from η unless β = 1.
For wear-out failures (β > 1), the time for a target reliability is a starting point for a preventive replacement or planned maintenance interval. With β ≤ 1, age-based replacement gains nothing; condition monitoring is the better tool there.
03
Why do censored records matter?
In field data many units have not failed yet: they are still running, were pulled for maintenance or were suspended for another reason. Dropping these records makes life look shorter than it is, because you only see the early failures. The right way is to enter them as censored (S).
For censored data the tool uses Johnson's adjusted rank: a censored unit pushes the ranks of later failures up partially. Bernard's approximation for the median rank, F = (rank − 0.3) / (n + 0.4), is then applied. If a failure and a censored record share the same time, the failure is counted first.
04
RRX and MLE: which one to trust?
Rank regression (RRX) fits a line to the points on probability paper; R² shows how well the line fits and the plot makes mixed failure modes easy to spot. It is widely used for small samples.
Maximum likelihood (MLE) takes censoring into account at the likelihood level and behaves well as the sample grows, but with very few failures it can bias β upwards. If the two methods agree you can trust the estimate more; if they differ, more data or a data-quality check is needed. The tool gives no confidence bounds; with a small sample the uncertainty is large.
FAQ
- Is the data I enter sent anywhere?
- No. The calculation runs entirely in code inside your browser; failure times are neither transmitted to a server nor stored.
- How many failures do I need?
- The tool requires at least 3 failures, but below 6 the results are very uncertain. Around 10 failures or more is generally recommended for a reliable β; since this tool gives no confidence bounds, read small-sample results as a rough direction.
- What is a censored (S) record?
- A unit that has not failed yet or left observation for a reason other than failure (maintenance, end of test, data cut-off). Its running time is known but its failure time is not; it is only known to be longer. Add S at the end of the line.
- What if β < 1 or β ≈ 1?
- β < 1 points to early-life failures and β ≈ 1 to random failures; in both cases age-based part replacement does not help. Focus on quality, commissioning, operating conditions and condition monitoring.
- What does B10 life mean?
- It is the time by which 10% of units are expected to fail, corresponding to 90% reliability. B1 and B50 follow the same logic for 1% and 50%.
- Which unit should I use?
- The unit that best explains the failure: operating hours for rotating equipment, cycles for parts that switch or start, km for vehicles. All records must use the same unit.
From Weibull to live equipment health
β and η from historical failures, combined with the SCADA and sensor stream, show which equipment needs attention and when. Let's talk about your data and equipment in a free discovery call.