Reliability Distributions

Requires a Wolfram Notebook System
Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.
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.
Contributed by: Joe O'Hara (March 2011)
Open content licensed under CC BY-NC-SA
Snapshots
Details
The lognormal failure distribution model is: .
The exponential failure distribution model is: .
The Weibull failure distribution model is: .
Permanent Citation