A Problem in Equipment Maintenance

There have been several publications dealing with the theory of semi-Markov processes, [1–6]. Most of these have been purely theoretical analyses, although it is realized that the theory has many potential applications, [4, 6], particularly to so-called “repairman” problems and to problems in reliability. Other work along these lines has recently appeared in the literature, [8–11]. These papers are concerned with the reliability of multi-state mechanisms [8], with surveillance plans, [9, 10] and with inventory problems. In particular, the work of Barlow and Proschan considers a model almost identical to our own, using renewal theory methods. Since the semi-Markov process can be considered to be a generalization of renewal theory, it is not surprising that such applications are the first to suggest themselves. It is the purpose of this paper to present an application of the theory of semi-Markov processes to a problem in maintenance theory and obtain results which we believe to be new. The body of this paper will consist of material relevant to the actual problem; a development of the theory as needed in our presentation will be found in the Appendix.