Weibull Analysis Tool – 2 & 3 Parameter Reliability

Analyze Life Data and Predict Failure Rates to Improve Equipment Reliability.

What is Weibull Analysis?

The Weibull distribution is the cornerstone of modern reliability engineering. Its flexibility to model decreasing, constant, and increasing failure rates through the shape parameter β makes it applicable to virtually any failure mechanism.

This tool goes further by including the advanced 3-parameter variant, which adds a location parameter γ (guaranteed failure-free period), useful when no failures can physically occur before a minimum time.

Available Methods: MLE, Regression & GoF

  • MLE (L-BFGS-B): Maximum Likelihood with multi-start L-BFGS-B optimizer. Handles exact, right-censored, and interval-censored data. Profile likelihood and Fisher CIs.
  • Linear Regression: Classic probability-plot method with Herd-Johnson adjusted ranks. Benard or Hazen plotting positions.
  • Monte Carlo GoF: Correct parametric p-value for the Anderson-Darling test, accounting for parameter estimation bias.
  • Parametric Bootstrap: Percentile CIs for β, η, B10, B50, MTTF using a fixed seed for reproducibility.

Toolbar — Button Reference

The toolbar at the top of the page contains all the actions you need to manage your analysis:

  • New   Clears all fields and starts a blank analysis.
  • Load   Opens a previously saved .json file and restores the input parameters.
  • Load Example   Loads pre-filled example data so you can explore the tool.
  • Analyze   Runs the Weibull analysis and generates the results and plots.
  • Save   Downloads the input parameters as a .json file.
  • Export PDF   Generates and downloads a fully formatted PDF report of the analysis results.

How to Use This Tool — Step by Step

  • Step 1 — Input Data: Go to the Calculator tab. Enter your failure times and any optional suspension (right-censored) or interval data.
  • Step 2 — Select Options: Choose between 2-Parameter or 3-Parameter analysis, select the calculation method (MLE or Regression), and adjust other parameters.
  • Step 3 — Run Analysis: Click the Analyze button to compute the Weibull parameters.
  • Step 4 — Review Results: Switch to the Results tab. Here you will find the estimated parameters, confidence intervals, B-Lives, and multiple distribution charts.
  • Step 5 — Save and Export: Click Save to store your input data for later use, or Export PDF to download a printable report.

Weibull Calculator

Weibull Analysis Calculator

3-Parameter Weibull γ ENABLED
Adds location parameter γ (guaranteed failure-free period). Smart fallback to 2P if likelihood is unbounded (β<1, γ→min(t)).
MLE (L-BFGS-B): Constrained quasi-Newton optimizer with multi-start. Handles exact, right-censored and interval-censored data. Profile likelihood & Fisher CIs.

Parametric simulation corrects the anti-conservative bias of the analytical AD p-value when parameters are estimated from data.

You can also click Analyze in the top toolbar from any tab.

Weibull Fit Results & Reliability Metrics

Estimated Weibull Parameters (β, η, γ)

Shape β —
Scale η —
MTTF —

Failure Mode

B-Life Percentiles

B10
—
B50
—
B90
—

Goodness‑of‑Fit & Model Adequacy

R² (prob plot) —
Log-Likelihood —
AIC —
BIC —
KS D —
KS p-value —
AD A²* —
AD significance —

Confidence Intervals (95% Profile Likelihood)

Profile Likelihood (Wilks)
β CI—
η CI—

Weibull Distribution Functions (PDF, CDF, Hazard, Reliability)

PDF f(t)

CDF F(t)

Hazard h(t)

Reliability R(t)

Descriptive Statistics of Failure Data

Weibull Formulas & Parameter Interpretation

Core Weibull Formulas

PDF

$$f(t)=\frac{\beta}{\eta}\left(\frac{t-\gamma}{\eta}\right)^{\beta-1}e^{-\left(\frac{t-\gamma}{\eta}\right)^\beta}$$

CDF

$$F(t)=1-e^{-\left(\frac{t-\gamma}{\eta}\right)^\beta}$$

Reliability

$$R(t)=e^{-\left(\frac{t-\gamma}{\eta}\right)^\beta}$$

Hazard Rate

$$h(t)=\frac{\beta}{\eta}\left(\frac{t-\gamma}{\eta}\right)^{\beta-1}$$

MTTF

$$\text{MTTF}=\gamma+\eta\,\Gamma\!\left(1+\frac{1}{\beta}\right)$$

B-Life

$$t_p=\gamma+\eta\left(-\ln(1-p)\right)^{1/\beta}$$

Parameter Interpretation

  • β < 1 — Decreasing failure rate (infant mortality, manufacturing defects)
  • β = 1 — Constant failure rate (random failures, exponential distribution)
  • 1 < β ≤ 3 — Increasing failure rate (wear-out, fatigue, corrosion)
  • β > 3 — Rapidly increasing failure rate (severe wear-out, tight distribution)
  • η — Characteristic life: 63.2% of units have failed by time η
  • γ — Minimum life: no failures occur before time γ (3P only)