Given an indexed family of rate functions, we construct a family of independent random variables such that their minimum and the corresponding index form a marked point having the same rates. If the rates have common discontinuities, the random variables are conditionally independent, given a random allocation of these jumps. Between any two adjacent points of a marked point process there is a similar structure. Coherent functions in system lifetime theory provide examples.
Non-identifiability of multivariate lifetime distributions from mortality data is interpreted in this context.