Necessary and Sufficient Condition for Optimal k-out-of-n Structure of Monitoring System with n General Sensors

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Jin et al. investigated the optimal maintenance problem for a monitoring system comprising multiple sensors and obtained a sufficient condition for a k-out-of-n structure to be optimal in terms of minimizing the expected risk. This research showed that their condition is not only sufficient but also necessary for a k-out-of-n structure to be optimal. Therefore, it is the only condition under which the optimal structure that minimizes the expected risk is a k-out-of-n structure. This means that, fewer structures need to be considered when searching for the optimal one. Moreover, the "k" for the optimal k-out-of-n structure has now been shown to be non-increasing in a prior state probability under the given condition. This makes the optimal structure more easily identifiable.

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