# Weibull Analysis of Component Reliability

*The Weibull model is remarkable for being able to provide insight in so
many situations. *

## The Ubiquitous Weibull Model

Observational data can be usefully summarized by fitting it with a probability distribution,
like the normal, lognormal or Weibull. For assessing component and system
reliability the most widely used is the Weibull distribution.

The figure below describes the fraction failing as a function of
service time. There were 70 items on test. 12 failed (shown as
black dots) and 58 were removed at various times prior to failure.
These are represented by the red tic-mark along the top of the plot.
The data are from Meeker and Escobar (1998), **Statistical Methods for
Reliability Data**, Wiley, Table C-1, p630.

*Figure 1 - A Weibull model for describing component failure data, 12
failures and 58 right-censored observations. *
(Data from Meeker and Escobar (1998), Table C-1)

The parameter estimates for the Weibull model (solid black line) were
determined using the maximum likelihood method. The dashed lines are
the 95% confidence bounds constructed using the loglikelihood ratio
criterion.

More about the analysis and graphics
software:

More about the
Properties of the Weibull model: