chapter  9
22 Pages

Random Point Processes in System Replacement

Point processes A point process is a sequence ft1; t2; g of real numbers with

t1 < t2 < and lim i!1

ti =1: That means, a point process is a strictly increasing sequence of real num-

bers, which does not have a …nite limit point. Generally, the ti are called event times or, more exactly, event time points. In reliability and maintenance theory, point processes are mainly generated by the failure time points of systems or by the time points at which repaired or renewed systems resume their work, given that the life and repair periods continue unlimitedly. Strictly speaking, since every repair-failure process will be stopped after a …nite time, the generated point processes have to be considered …nite samples from a point process.