A stochastic process concerned with the times of replacement of components that are replaced as soon as they break down. Suppose a system has a single component, which is replaced immediately when it breaks down. Suppose the jth component has a lifetime Xj. The time, Tj, at which this component breaks down is given by
The sequence T1, T2,…is a renewal process. A useful result is that, if N(t) is the number of breakdowns by time t then
Subjects: Probability and Statistics.