Reliability Distributions

failure distribution model

lognormal

exponential

Weibull

lognormal model parameters

μ

0.5

σ

1

exponential model parameter

λ

1

Weibull model parameters

α

0.5

β

1

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

f(t)

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

μ

and

σ

for the lognormal,

λ

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

F(t)

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

h(t)

=

f(t)

1-F(t)

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

1-F(t)

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