Optimal abort rules for additive multi-attempt missions

Abstract

Mission aborts can be executed in many real-world systems when the specified malfunction/deterioration conditions are met and, therefore, a risk of a system's loss in the case of mission continuation becomes too high. After mission aborting, a rescue or recovery procedure is usually initiated. Previous results reported in the literature dealt with the setting when only one attempt to complete a mission is allowed. However, missions with a possibility of multiple attempts can occur in different real-world settings when accomplishing a mission is really important and the cost-related and the time-wise restrictions for this are not very severe. In this paper, we consider the case when a part of the mission task that was accomplished in the earlier attempts can be saved (additively) and not discarded. The probabilistic model for this case is developed and the tradeoff between the overall mission success probability and the system loss probability is studied. The problem of achieving the maximal mission success probability for the given level of system survivability is solved. A detailed example illustrating application of the suggested model is presented. It is shown that, unlike the single attempt case, aborting the mission when multiple attempts are allowed, can be beneficial even when the mission completion is the only concern and no constraint is imposed on the system survival probability.