How does our degrading system perform?

We discuss the quality of performance of degrading systems when degradation is modeled by a stochastic process with independent increments and increasing sample paths. As an example, the gamma process is considered. First, for the continuously observed degradation, by comparing with the black-box scenario (without observing degradation), the new operational curve as a function of mission time is defined and described. This curve divides degradation space into two regions. If the observed degradation is larger than the value of this function at some time instant, then the performance can be considered as unacceptable/risky and the option of aborting a mission or other interventions can become relevant. For justifying the abort option, a new cost-wise model is suggested that considers the cost of system maintenance after abort or completion of a mission. The corresponding optimization problem providing the optimal time of inspection and the optimal level of a degradation threshold at inspection for initiating abort is formulated. Numerical examples with discussion illustrate our findings.