This paper presents a general framework for analysing condition based
replacement policies for stochastically failing units. The framework i
s based on the theory of counting processes. A replacement policy mini
mizing the long run expected cost is determined. The paper discusses b
oth non-repairable and repairable units. Two examples are analysed in
detail: shock models and monotone (coherent) systems. (C) 1996 Elsevie
r Science Limited.