Anomaly Detection of Functional Data via Conformal Prediction

We propose a novel methodology for detecting anomalies in the monitoring of profiles in industrial processes. Our approach is grounded in functional data analysis. Theoretically, we guarantee the control of the probability of having one or more false anomalies along the functional domain also in the case of small sample sizes and non-Gaussian data which are common for instance in bioprinting applications. The functional control limits are obtained by inverting simultaneous functional conformal prediction bands which have been recently proposed in the literature. The concept of conformal p value function is introduced and its applicability is shown in an industrial application in the field of bioprinting of synthetic skin.