Management decisions regarding maintenance protocols critically hinge on the underlying probability
distribution of the time between failures in most repairable systems. Replacement of the system with
a new one resets the system age to zero, whereas a repair does not alter the system age but may shift
the parameters of the failure-time distribution. Additionally, maintenance decisions lead to left-truncated
observations, and right-censored observations. Thus, the underlying stochastic process governing a
repairable system evolves based on the management decision taken.
This paper mathematically formalizes the notion of how management actions impact the functioning
of a repairable system over time by developing a new stochastic process model for such systems. The
proposed model is illustrated using both simulated and real data. The proposed model compares favorably
to other models for well-known data on Boeing airplanes. The model is further illustrated and compared
to other models on failure time and maintenance data stemming from the South Texas Project nuclear
power plant.