5.3.6 __Weibull Distribution__

The Weibull distribution is particularly useful in reliability
work since it is a general distribution which, by adjustment of the
distribution parameters, can be made to model a wide range of life
distribution characteristics of different classes of engineered items.

One of the versions of the failure density function is

where:

b is the shape parameter

h
is the scale parameter or characteristic
life

(life at which 63.2% of the population will have
failed)

g is
the minimum life

In most practical
reliability situations, g is often zero (failure assumed to start at t = 0) and
the failure density function becomes

and the reliability and hazard functions
become

Depending upon the value of
b, the Weibull
distribution function can take the form of the following distributions as
follows,