Renewal processes and applications

In the introductory Chap. 2, we have already given and discussed the definition of the renewal process. In this section, for consistency, we first define and discuss this process in more detail and then consider its main properties. The special emphasis is on asymptotic relations for the main functions of interest that are essential for presentation in this book. For instance, in subsequent chapters, we will consider various optimal maintenance problems that will rely on the important Renewal Reward Theorem to be discussed in this chapter. Then we present several important applications, where we illustrate how renewal principles and reasoning are applied to different reliability problems. Obviously, we do not aim at systematic description of renewal theory but presenting some basic facts to be used in what follows. Some generalizations of the ordinary renewal process will be considered in Chap. 7.