Many industrial systems require specific missions to be performed during a given time period. The chance of mission success, meaning the probability of completing a particular mission with or without a deadline, is an important metric used to eva‎luate the performance of mission-based systems. However, for critical-safety systems such as airplanes, submarines, and unmanned aerial vehicles, the survival of the system in the face of failure is a higher priority than achieving a successful mission, because a malfunction in such systems can result in significant economic damages and environmental risks. In such cases, when a failure or a specific incident occurs, the mission can be abort immediately to avoid catastrophic system failures, and rescue procedures can be initiated pro‎mp‎tly to reduce the risks of system failure. Common metrics used to eva‎luate the random behavior of these systems include mission reliability, which is equal to the probability of successful mission completion, and system survival probability, which is the probability of the system surviving without experiencing any catastrophic failures. Increasing the system survival probability through mission abort leads to a decrease in mission reliability. Therefore, optimal design of a mission abort policy, which takes into account the system failure characteristics and aims to balance a trade-off between the two metrics of mission reliability and system survival probability, is highly valuable in practice. In engineering operations, operators can usually identify some of the warning signals of malfunction, such as excessive vibration, overheating, cracking, rupture, etc. Systems with such failure mechanisms are usually modeled with a two-stage degradation process, where the first stage is from the start of the new system until the onset of failure, and the second stage is from the onset of failure to the point of system breakdown. This thesis presents mission abort policies for systems that are subject to two-stage degradation processes. A two-stage gamma process is considered to describe the normal and defective stages of the system to model the system failure process. To optimize the mission abort policy for these systems, two abort policies are introduced: a degradation-based abort policy where the mission is aborted when the degradation level exceeds a certain threshold, and a duration-based abort policy where the mission is stopped when the time spent in the defective state exceeds a certain threshold. The main objective is to find the optimal time duration in the defective state after which the mission should be stopped and rescue procedures should start immediately. The optimization problem addressed is formulated as the minimization of economic losses and damages as the objective function. In another section of the thesis, it is assumed that the aforementioned system, which is subject to a two-stage degradation process, is also subject to random shocks. The proposed approach for incorporating the effect of shocks on the system is to assume that the system ages faster when a shock occurs, and thus its virtual age exceeds its calendar age. For this system, a mission abort policy is also defined, and then the optimal design of this policy is investigated through an optimization problem. The optimization problem aims to find the optimal time to abort the mission after a shock occurs, given the system’s current virtual age and the economics loss of the mission. The objective is to minimize the expected economic loss due to mission failure and system breakdown. The resulting optimal mission abort policy can help operators make informed decisions about when to abort a mission after a shock occurs.

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