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Environmental safety issues are of particular importance when we design and operate underwater transport systems. To ensure the transport systems function safely, special systems to monitor their condition are being created. Underwater pipeline monitoring systems should continuously operate to detect and prevent emergency and pre-emergency situations in a timely manner. The purpose of this article is to demonstrate the possibility of using a mathematical model of a k-out-of-n system to support decision-making in the preventive maintenance of an unmanned underwater vehicle to monitor the condition of a subsea pipeline. The novelty and feature of this study are that we investigate a strategy of preventive maintenance for a model of a k-out-of-n system, where failures depend not only on the number but also on the location of the failed components in the system. The method to solve this problem, based on the distribution of the members of the variational series of the failing components, is also new. Since the distributions of the system component lifetimes are usually known with an accuracy of only one or two moments, we paid special attention to how sensitive the decision making about preventive maintenance is to the shape of the distributions. Numerical examples are conducted in order to support the theoretical investigations of the paper. The results of the study are applied to specific equipment to monitor the state of the outer surface of the pipeline.

Preventive Maintenance of a k-out-of-n System with Applications in Subsea Pipeline Monitoring