OPTIMUM REPLACEMENT OF A SYSTEM SUBJECT TO SHOCKS

A system is subject to shocks. Each shock weakens the system and makes it more expensive to run. It is desirable to determine a replacement time for the system. P. J. Boland and F. Proschan 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 does not depend on time. H. W. Block et al. establish similar results assuming that cost structure is time dependent, still requiring that the shock process is a non-homogeneous Poisson process. We show via a sample path argument that both sets of results hold for any counting process whose jump size is of one unit magnitude.