Optimal aborting strategy for three-phase missions performed by multiple units

It is often reasonable to abort a mission before its completion if the consequences of a failure in the rest of a mission time outweigh the potential benefits. This paper considers the multi-attempt missions that are performed by a multi-unit system when each unit independently can complete a mission. To model the real-life situations when the successful completion of the operation phase does not guarantee the mission success, a post-operation final phase is introduced. A mission succeeds if, at least, one of the units succeeds to complete this final phase. A unit can start the new attempt if it has been saved during the rescue phase activated upon the operation abort or after completing the previous attempt that did not achieve a mission goal. A system operates in a random environment modelled by a shock process. Units can fail under shocks with probabilities increasing with the number of survived shocks. The maximum number of shocks allowed before the mission abort is used as the optimization parameter for the optimal aborting strategy that achieves the balance between the mission success probability and the expected number of units lost while executing the mission. The developed approach is illustrated by the detailed examples showing, specifically, that the optimal number of attempts under the risk-avert policy can be obtained along with the optimal abort policy.