Cox D.R. Renewal Theory

Methuen, 1962. — 142 p.Renewal theory began as the study of some particular probability problems connected with the failure and replacement of components, such as electric light bulbs. Later it became clear that essentially the same problems arise also in connexion with many other applications of probability theory and moreover that the fundamental mathematical theorems of renewal theory are of intrinsic interest in the theory of probability. Hence much recent work in the subject is not specifically connected with the replacement of components. At the same time, however, with the current surge of interest in the mathematical problems of operational research, new problems connected with the replacement of components have been formulated, not all within the framework of renewal theory in the original sense.
The plan of this monograph is as follows. In Chapters 2-5 we deal with the principal general formulae of renewal theory. These will be treated from an applied mathematical point of view; that is, we do not give rigorous proofs of the results under the most general conditions possible. In Chapters 6-9 some extensions of the fundamental models of renewal theory are given. Chapters 1-9 form a self-contained course in renewal theory for those whose interest is in applied probability theory, not necessarily in connexion with operational research.
Chapters 10 and 11 are more specialized. Chapter 10 deals with models of failure. Chapter 11 discusses a number of problems connected with the replacement of components, in particular with the study of replacement strategies. Problems of statistical analysis connected with renewal theory are not considered in this monograph.