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Achieving resilient and high-quality manufacturing requires reliable data-driven anomaly detection methods that are capable of addressing differences in behaviors among different individual machines which are nominally the same and are executing the same processes. To address the problem of detecting anomalies in a machine using sensory data gathered from different individual machines executing the same procedure, this paper proposes a cross-machine time-series anomaly detection framework that integrates a domain-invariant feature extractor with an unsupervised anomaly detection module. Leveraging the pre-trained foundation model MOMENT, the extractor employs Random Forest Classifiers to disentangle embeddings into machine-related and condition-related features, with the latter serving as representations which are invariant to differences between individual machines. These refined features enable the downstream anomaly detectors to generalize effectively to unseen target machines. Experiments on an industrial dataset collected from three different machines performing nominally the same operation demonstrate that the proposed approach outperforms both the raw-signal-based and MOMENT-embedding feature baselines, confirming its effectiveness in enhancing cross-machine generalization.