Statistics for Maintenance Modelling: Repairable Systems

# Non-homogeneous Poisson Process Models (NHPP)¤

The mean time between failures is 1/. A system for which we expect the HPP to be a good model is one in which there are many components liable to fail, but the probability of failure of any one of them is small. In applications, assumption 2 (on the previous screen) is critical. Many systems are in practice either improving or deteriorating with time. In this case we need more general models, and the NHPP is one of them.

The assumptions for a NHPP are as for the HPP except that the ROCOF varies with time. Consider a NHPP with a time-dependent ROCOF, (t), then the number of failures in the interval (t1, t2] has a Poisson distribution with mean:

E(N(t1, t2)) = (t) dt

Thus the probability of having k failures in (t1, t2] is:

P(N = k) = ( (t) dt)k / k!

When k = 0, we have the probability of no failures in (t1, t2] given by:

P(N = 0) =

By choosing a suitable parametric form for (t), one can obtain a flexible model for the failures of a repairable system in a 'minimal repair' set-up, i.e. when only a small proportion of the component parts of the system are replaced on repair.