Some Applications of Regenerative Stochastic Processes to Reliability TheoryߞPart One: Tutorial Introduction

After a brief introduction to the general concept of regenerative processes and to some applications of these processes to reliability theory, this first part of a two-part paper investigates the renewal process and, subsequently, the alternating renewal process. Both these processes are basic regenerative processes and constitute the mathematical model of a renewable item. The investigation deals carefully with those quantities and theorems which are of particular interest for reliability theory and which will be used in the second part of the paper. A brief review of the literature dealing with repairable systems containing redundancy, as well as a description of an alternative investigation method is given in an appendix.