1. __When to Use__. The flexibility of the Weibull
distribution makes it useful in describing the probability density function
for a variety of cases. The Weibull cumulative distribution function is given
by:

The Weibull distribution is used to
describe the distribution of times to failure and of strengths of brittle
materials, and the weakest link phenomena. It is an appropriate failure law
model whenever the system consists of a number of components, and failure is
essentially due to the “most severe” fault
among a large number of faults in the system. By making an appropriate choice
of the shape parameter, b, either an increasing or a decreasing failure rate can
be obtained. Estimates of the Weibull shape (b) and scale (q) parameters may be obtained
graphically using *ln-ln
*(or a special Weibull probability)
graph paper. Less accurate than statistical methods, this method can be done
quickly and easily.

2. __Steps in Using the Graphical
Method__

3. __Example__

The following failure data are
collected from a test in which 20 items were tested to failure.