A decision dependent stochastic process model for repairable systems with applications

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.