Compartmental modelling of equipment subject to partial repair

A semi-Markov model for equipment that can be repaired and returned to service in a less than new state is developed, where several less than new states are possible before the equipment finally fails. A subclass of phase-type distributions is used to model the times spent in each of these states. Then, exploiting the phase-type structure, the composite distribution of the entire lifetime of the equipment can be constructed. Data from railway wagon wheel-sets are used to illustrate this modelling and data analysis.