Anomaly detection is a learning task in which anomalies are extremely less frequent than the normal behaviour. We aim at detecting anomaly, actually fluid leakage, as soon as possible, before a preventive shutdown of the machine. In this article, we study the resistance to noise and to rarity of anomalies of a supervised learning technique, decision trees. We consider arti- ficial data representative of physical system anomalies such as a tire puncture or a refrigerant leak from a heat pump. Our tests show that a decision tree is able to learn a threshold on the pressure observed, in the presence of noise, which adapts to very low frequencies of anomalies, down to 1 per 100,000.