Model of bus electrical system failure process

The lifetime distribution is important in reliability studies. There are many situations in lifetime testing, where an item (technical object) fails instantaneously and hence the observed lifetime is reported as a small real positive number. Motivated by reliability applications, we derive the branching Poisson process and its property. We prove that the branching Poisson process is adequate model for the failure process of the bus electrical system. The method is illustrated by two numerical examples. In the second example, we derive the times between the failures of a bus electrical system.