Weibull Analysis

Weibull analysis is a statistical method for modelling time-to-failure data with the Weibull distribution, whose shape parameter shows whether failures are early-life, random or wear-out, and whose scale parameter gives the characteristic life.

The Weibull distribution, named after the Swedish engineer Waloddi Weibull, is flexible enough to describe many failure patterns. In its common two-parameter form, the shape parameter beta describes how the failure rate changes with age: beta below one indicates a decreasing failure rate typical of early-life failures, beta equal to one a constant rate, as in the exponential distribution, and beta above one an increasing rate typical of wear-out. The scale parameter eta, the characteristic life, is the age by which about 63.2 per cent of a population is expected to have failed. A three-parameter form adds a location parameter for a failure-free period.

Engineers fit Weibull models to failure times from field data or life tests, traditionally by plotting on Weibull probability paper and now with software using regression or maximum likelihood estimation. The results support decisions on preventive replacement intervals, warranty forecasting, spare parts demand and design comparisons, and help determine whether a time-based task suits a failure mode.

Reliable analysis requires each data set to represent a single failure mode, because mixing modes distorts the parameters. Units still running, called suspensions or censored data, must be included correctly, and small samples give wide confidence bounds. When beta is close to one, time-based replacement brings little benefit, and condition-based or run-to-failure strategies are usually considered instead.

Key points

Shape parameter below one: early-life; equal to one: random; above one: wear-out.
Characteristic life is the age by which about 63.2 per cent have failed.
Named after the Swedish engineer Waloddi Weibull.
Each analysis should cover one failure mode and include suspensions.

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Related terms

Terms that refer to Weibull Analysis

Mean Time Between Failures (MTBF)Quality, Reliability & Maintenance