Three repair options depending on failure time for a system with administrative delay

A maintenance policy depending on failure occurrence time is proposed. Supposing a system equipped on a vehicle such as a vessel, which conducts a fixed period of mission like a voyage, we propose three options for a failure of a system occurred during the mission: (A) return to the base from which the vehicle departed and repair there, (B) instantaneous repair on-site and (C) to leave the failure and repair it after the end of the mission. Exponential distribution is supposed as the failure occurrence distribution of the system. Our goal is to determine the optimal action depending on the occurrence time of failures, where the optimal policy minimizes the expected cost until the completion of one mission, ensuring a certain mean availability.