Module 1 · 3 hours
Weibull Failure Analysis
The Weibull distribution is the standard statistical model for mechanical failures. This module teaches the math, how to fit a curve to field data, and how to read the shape parameter to diagnose a fleet's life stage.
Learning Objectives
- Write the Weibull CDF and PDF and explain each parameter
- Fit a Weibull distribution to censored field data
- Interpret β: infant mortality (β<1), random (β=1), wear-out (β>1)
- Project end-of-life timing for a fleet population
The Weibull equation
F(t) = 1 − exp(−(t/η)^β), where η = scale parameter (characteristic life) and β = shape parameter.
The characteristic life η is the time at which 63.2% of the population has failed — a robust way to describe the life of a mechanical component.
β tells you what kind of failure regime you are in: quality defects, random events, or true wear-out.
Reading β in the field
β < 1: early-life failures dominate. Usually quality escapes or infant mortality. Fix: tighten acceptance testing at receiving.
β ≈ 1: constant hazard rate. Failures are essentially random. Fix: redundancy or faster replacement.
β > 1: wear-out. Probability of failure rises with age. Fix: scheduled replacement before the knee of the curve.