Optimal stopping problems for mission oriented systems considering time redundancy

•Novel mission abort models considering two types of time redundancy are established.•Dynamic mission abort policy is developed where the abort threshold varies with mission attempts.•Mission reliability and system survivability are derived under two types of time redundancy.•The optimal abort thresholds minimizing the expected cost of mission failure and system failure are investigated. Catastrophic failures of safety-critical systems could result in irretrievable economic losses and damage. To enhance the survivability of safety-critical systems, a mission can be terminated if the failure risk becomes too high. Time redundancy can be commonly observed in many practical systems where missions can be executed multiple times during a constrained time to improve the mission reliability. This paper investigates the optimal mission abort policies for systems with continuous degradation considering two types of time redundancy. Under type I time redundancy, the system should keep operational continuously for a time period greater than a specific value. In the second case, mission success requires that the cumulative working time should be greater than the given value. Dynamic mission abort decisions are considered based on the degradation level and mission attempts. Mission reliability and system survivability are derived under two types of time redundancy. The optimal mission abort threshold in each attempt is investigated to minimize the expected total cost of mission failure and system failure. A case study is presented to illustrate the obtained results.