  We explore the concept of a consistent exchangeable survival process - a
joint distribution of survival times in which the risk set evolves as a
continuous-time Markov process with homogeneous transition rates. We show a
correspondence with the de Finetti approach of constructing an exchangeable
survival process by generating iid survival times conditional on a completely
independent hazard measure. We describe several specific processes, showing how
the number of blocks of tied failure times grows asymptotically with the number
of individuals in each case. In particular, we show that the set of Markov
survival processes with weakly continuous predictive distributions can be
characterized by a two-dimensional family called the harmonic process. We end
by applying these methods to data, showing how they can be easily extended to
handle censoring.
