Network Function Virtualization is an emerging paradigm to allow the creation, at software level, of complex network services by composing simpler ones. However, this paradigm shift exposes network services to faults and bottlenecks in the complex software virtualization infrastructure they rely on. Thus, NFV services require effective anomaly detection systems to detect the occurrence of network problems. The paper proposes a novel approach to ease the adoption of anomaly detection in production NFV services, by avoiding the need to train a model or to calibrate a threshold. The approach infers the service health status by collecting metrics from multiple elements in the NFV service chain, and by analyzing their (lack of) correlation over the time. We validate this approach on an NFV-oriented Interactive Multimedia System, to detect problems affecting the quality of service, such as the overload, component crashes, avalanche restarts and physical resource contention.