Statistics for Maintenance Modelling: Continuous Lifetime Distributions 1

# Relating the Poisson Distribution to the Hazard Function¤

The reliability (survivor) function is the probability that there are no failures in an interval of length t, i.e.:

The failure probability density function is the derivative of minus R(t) with respect to time, so:

(This is the exponential distribution. For more, see the Weibull distribution on screen 16.)

Therefore the hazard rate is:

Hence the hazard rate is constant, i.e. an item's age does not affect its chance of failing.

We have actually been discussing what is referred to as a homogeneous Poisson process as time intervals of the same length are treated in the same way. Click here to learn about non-homogeneous Poisson processes.

And click here to find out how the Poisson distribution can model the binomial distribution.