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This paper introduces an active learning (AL) framework for anomalous sound detection (ASD) in machine condition monitoring system. Typically, ASD models are trained solely on normal samples due to the scarcity of anomalous data, leading to decreased accuracy for unseen samples during inference. AL is a promising solution to solve this problem by enabling the model to learn new concepts more effectively with fewer labeled examples, thus reducing manual annotation efforts. However, its effectiveness in ASD remains unexplored. To minimize update costs and time, our proposed method focuses on updating the scoring backend of ASD system without retraining the neural network model. Experimental results on the DCASE 2023 Challenge Task 2 dataset confirm that our AL framework significantly improves ASD performance even with low labeling budgets. Moreover, our proposed sampling strategy outperforms other baselines in terms of the partial area under the receiver operating characteristic score.