Online anomaly detection of profiles with varying coefficients via functional mixed effects modelling

In this paper, a novel online sequential monitoring scheme is proposed for real-time detection of anomalies in the incoming profile data. A profile data, in the present context, consists of the response affected by multiple time-dependent covariates and is subject to within-profile correlation. The proposed scheme is based on a functional mixed-effects model, where the response variable is influenced simultaneously by functional fixed-effect and random-effect terms. The baseline functional mixed-effects model is first estimated based on in-control historical profiles during appropriate Phase-I analysis. Subsequently, a Phase-II exponentially weighted moving average scheme is implemented using a monitoring statistic based on penalized spline smoothing for sequential monitoring of the online profile data. Theoretical results and extensive simulation studies show the effectiveness of the proposed charting scheme. Moreover, the proposed method is validated by an application example from the drying process of tobacco manufacturing. Technical details are given in the Appendix.