Anomaly detection in time series has become a widespread problem in the areas such as intrusion detection and industrial process monitoring. Major challenges in anomaly detection systems include unknown data distribution, control limit determination, multiple parameters, training data and fuzziness of ‘anomaly’. Motivated by these considerations, a novel model is developed, whose salient feature is a synergistic combination of statistical and fuzzy set-based techniques. We view anomaly detection problem as a certain statistical hypothesis testing. Meanwhile, ‘anomaly’ itself includes fuzziness, therefore, can be described with fuzzy sets, which bring a facet of robustness to the overall scheme. Intensive fuzzification is engaged and plays an important role in the successive step of hypothesis testing. Because of intensive fuzzification, the proposed algorithm is distribution-free and self-adaptive, which solves the limitation of control limit and multiple parameters. The framework is realized in an unsupervised mode, leading to great portability and scalability. The performance is assessed in terms of ROC curve on university of California Riverside repository. A series of experiments show that the proposed approach can significantly increase the AUC, while the false alarm rate is improved. In particular, it is capable of detecting anomalies at the earliest possible time.