Difference Between Mean Life and Characteristic Life

[Ed Smith]

Is the mean life the same as the characteristic life for the Weibull distribution (regardless of shape parameter beta)?

[Dennis Craggs]

The characteristic life is a parameter of the Weibull distribution. Consider the two parameter weibull formula:

F(t) = 1 - exp(-(t/eta)^beta) where

t is time
F(t) is the fraction failed
eta is the characteristic life
beta is the shape factor (or slope)

The if t = eta, the formula reduces to

F(eta) = 1 - exp(-1) = 0.632

This means 63.2% of the population will fail when t = eta.

The mean is the expected life. This is calculate by integrating from 0 to infinity the product of the life x the probability density. This formula can be reduced to

mean life = eta * Gamma (1 + 1/beta)

where Gamma is the Gamma function. The Gamma function may be calculated using tables or popular spread sheets include a gamma function.

Look at http://www.weibull.com/AccelTestWeb/weibull_distribution.htm for a summary. Reliability text books will also contain this information.