Starting with the life fraction rule proposed by Robinson in 1952, a new phenomenological method has been developed for the prediction of damage accumulation processes involving creep, fatigues and wear phenomena. It is shown that by formal generalization of the conventional Robinson's rule, various types of differential equations can be generated which are applicable to the prediction of the progress of cumulative damage processes under conditions of variable external control parameters (load, pressure, temperature, etc). The applicability of this new approach to derive generalized wear evolution equations will be demonstrated by calculated results obtained by computer simulation.