A counting process approach to replacement models

In this paper we present a common set-up for a large class of replacement models for stochastically failing systems. The set-up is based on the theory of counting processes, The replacement rule which minimizes "the total expected discounted cost" is determined. Several shock models are included as special eases, for example a shock model for a system which is repaired (and not replaced) at failures, and a shock model for a coherent system.