Is our mission profitable: The cost-effectiveness curve with a possibility of a mission abort

We consider missions of fixed and random duration and are interested in their cost-effectiveness at each instant of time. As a measure of quality, the difference between the expected conditional profit (on condition that a system is operable at the current time) and a profit already earned up to this time in case of a mission abort is suggested. This takes into account the corresponding penalties and rewards due to abort or completion of a mission, respectively. However, the main focus is on cost-effective missions and requirements for achieving it. As a result, the cost effectiveness curve is obtained for two cases: with and without observing a univariate degradation process of a system. Specifically, when the degradation is observable, the cost effectiveness curve (at each instant of a mission time) indicates the value of degradation on exceeding which, a mission becomes non-profitable with respect to the suggested criterion. The detailed numerical examples illustrate our findings.