Reliability planning · Weibull analysis
Weibull Reliability Calculator
Plan or evaluate a zero-failure reliability demonstration using R, C, β, sample size, and test exposure.
GuideRequired test plan
Enter R and C as fractions: 0.95 = 95%.
Plan a zero-failure reliability test to demonstrate the selected reliability and confidence targets.
Demonstration result
Sample Size Matrix
Same R, C, and β as the current Calculator plan.
| Sample size n | Lives / sample | Total unit-lives | Achieved confidence | Rounded test lives | Confidence at rounded lives |
|---|
Enter valid Calculator plan inputs to generate the matrix.
Rounded test lives are conservatively rounded up to the next 0.1 life. The planned sample size is highlighted in maize. Converted physical exposure uses the conservatively rounded test duration.
Weibull Fit
Estimate β and characteristic life η with a probability plot or maximum likelihood.
Failure-life observations
Positive values in one consistent unit.
| Specimen | Life / cycles | Status | Row action |
|---|
Paste a single Excel column into any life or exposure cell. Existing row statuses are preserved; newly created rows default to Failure. Hours, miles, cycles, or another consistent positive exposure unit are acceptable.
Suspension caution: right-censoring should reflect a stopping reason unrelated to impending failure.
Import provenance
Ranked and transformed data
| Specimen | Failure life | Rank | Median rank F | ln(life) | ln[-ln(1-F)] |
|---|
A valid fit will populate the ranked analysis.
Weibull fit
Small failure populations can produce unstable Weibull estimates. Use the fit as an engineering estimate and prefer additional representative failures when available.
Enter at least three complete failure lives to estimate β and η.
Distribution predictions
Point estimates from the fitted β and η.
Reliability at mission life
Enter a life requirement; zero is allowed.Life at target reliability
Use a decimal between 0 and 1.B-life and MTTF values use the current Fit unit. Parameter confidence bounds are not included.
Complete a valid Weibull fit to calculate life metrics and distribution predictions.
Weibull probability-plot regression
Observed ranks and fitted line.
Fit scope & assumptions
This fit uses complete failure-life observations and Bernard median ranks, Fᵢ = (i − 0.3) / (n + 0.4). The Weibull probability transform is fit by ordinary least squares. The regression slope estimates β and the intercept determines characteristic life η.
Point-estimate scope: β and η are point estimates. Parameter confidence intervals are not included.
- Two-parameter Weibull model; no location parameter
- Probability Plot requires complete failures; MLE supports right-censored suspensions
- Independent specimens from a common population
- Consistent exposure units; η is reported in the same unit
- R² is shown only for Probability Plot and is not a formal goodness-of-fit test
- No left censoring, interval censoring, location parameter, or confidence bounds
Suspension caution: suspensions should reflect a planned test ending or another stopping reason unrelated to the specimen’s impending failure; selective removal of deteriorating specimens can bias the analysis.
Failure-mechanism caution: a single fit is most meaningful when observations represent the same underlying population and dominant failure mechanism. Mixed failure modes can distort β.
η interpretation: at t = η, cumulative failure probability is approximately 63.2% and reliability is approximately 36.8% under the fitted model.