Optimal inspection for missions with a possibility of abortion or switching to a lighter regime

Many real-world critical systems, e.g., aircrafts, manned space flight systems and submarines, complex technological processes utilize mission aborts to enhance their survivability. Specifically, a mission can be aborted when a certain malfunction condition is met and a rescue or recovery procedure is then initiated. In this paper, we consider systems with observed degradation when a decision to abort a mission or to continue operation is executed at inspection. If this degradation is larger than the optimally predetermined level, then a mission is aborted, whereas if it is smaller, a system continues its operation either under the initial (full load) regime or under the lighter regime with the decreased load. The latter option also depends on the observed value of degradation at inspection. An optimal problem minimizing the expected costs with respect to the relevant levels of deterioration and inspection time is formulated and analytical relationships for the probabilities of interest and expected cost rates are derived. A new virtual age-based approach to age recalculation after the switching of regimes is proposed. A detailed illustrative example is presented.