Optimum Replacement of a System Subject to Shocks

摘要

A system is subject to shocks which cause the system to deteriorate. In previous studies, distribution properties of such systems are discussed for different types of deterioration processes. At best these processes are right continuous Markov processes. Our interest in this paper is to tackle a related but different problem: we assume that the normal cost of running the system is 'a' per unit of time and that each shock to the system increases the running cost by 'c' per unit of time. The cost of completely replacing the system is c sub 0. The system is to be completely replaced at times T, 2T, ..., . Such replacement policies are known as periodic replacement policies. Since each shock weakens the system and makes it more expensive to run, it is desireable to determine a replacement time for the system. Boland and Proschan (4) consider periodic replacement of the system and give sufficient conditions for the existence of an optimal finite period, assuming that the shock process is a non-homogeneous Poisson process and the cost structure is time dependent, still requiring that the shock process is a nonhomogeneous Poisson process. We show, via a sample path argument, that the results of (3) and (4) hold for any counting process whose jump size of one unit magnitude.