ABSTRACT
In Chapter 2, we dealt mostly with the time to failure (TTF) of nonrepairable objects. Considering different damage models resulting in special classes of TTF distributions (increasing failure rate (IFR), decreasing failure rate (DFR), etc.) and particular TTF distributions (such as the exponential distribution and Weibull distribution), we assumed that the damage was done by some random damaging events. The occurrence of these events is modeled by some random process (mostly by the homogeneous Poisson process (HPP) and the nonhomogeneous Poisson process (NHPP)). In this chapter, we discuss these processes in detail, concentrating on their properties and considering the damage made by each event. The main question we are going to address is: If the TTF distribution of an object (system) before the damaging event is F0(t), what is the TTF distribution just after the event? Is it the same distribution F0(t), or is it another distribution, say, F1(t)? If it is another distribution, how is it related to F0(t)?
