Statistics for Maintenance Modelling: Renewal Processes

# Definition of the Renewal Process¤

Consider a renewal process (e.g. of light bulbs). Then we can define:

- the renewal counting process as {N(t), t 0}, where N(t) is the number of events (e.g. failures) by time t, where intervals between events are i.i.d. (independent and identically distributed) random variates with pdf. f(x), distribution function F(x), survival function S(x).
- the intervals between failure times X1,...,Xn where n 1
- the waiting time to the nth event as the quantity Wn = X1 + ... + Xn, where n 1

Then {Wn, n 0} and {N(t), t 0} are called the renewal process.

This is illustrated on the right for the renewal counting process N(t), failure times X and waiting times W.