Failures over time for certain electronics products have been modeled by probability distribution functions,

, of at least three types: lognormal, exponential and Weibull. This Demonstration shows how the probability distribution functions appear with varying values of the parameters (

and

for the lognormal,

for the exponential, and α and β for the Weibull distributions). The shapes of the cumulative failure distribution functions,

, for these failure distributions are also shown. Also shown are curves for the hazard rate, or the instantaneous failure rate,

=

, which is the ratio of the failure distribution to the so-called survival distribution,

. Note that for proper selection of the parameters, the exponential distribution is a special case of the Weibull distribution.