Statistics for Maintenance Modelling: Renewal Processes

# What is a Renewal Process?¤

Imagine a light bulb, which has a probability density function of f(x), lasting for time x before it fails. When it fails, it is immediately replaced with a new one. The successive intervals between failures are random variables X1,...,Xn, and these form a renewal process. The candles shown here illustrate a similar scenario.

The main application of renewal processes is in reliability and replacement. In addition, they crop up constantly when considering other more complex stochastic processes. The recognition of an embedded renewal process and the application of the relevant theory is then an important step in solving the complex problem.

In this session, you will learn what a renewal process is, how the renewal function can be calculated, and how it is used in simple replacement models.

Can you think of any other examples of renewal processes in daily life? Click here to see some of our ideas.