Statistics for Maintenance Modelling: Renewal Processes

# Summary¤

A renewal process is best exemplified by the successive failures of a light bulb --- a series of failures where the interfailure period is a random variable from some distribution. An understanding of renewal processes is needed for simple replacement models, such as block replacement. The key concept is the renewal function: the expected number of renewals to some time t.

This session has explained how to do several calculations with renewal functions, but the most practical is the numerical calculation of the renewal function using the integral equation. For those who like discrete time approximations, a maintenance problem example is given where the problem is solved in discrete time.

It is probably best for study to at least read the introduction to this session, but not to bother too much about the details, and to then come back to it later if and when more detail is needed to solve particular maintenance problems.