Sometimes the quality of a process is best expressed by a relationship between response
variables and explanatory variables. Checking over the time the stability of such functional …

Functional data analysis has been a popular statistical research topic for the past three
decades. Functional data are often obtained by observing a number of subjects over time …

Process monitoring and fault diagnosis using profile data remains an important and
challenging problem in statistical process control (SPC). Although the analysis of profile data …

Over the past decades, control charts, one of the essential tools in Statistical Process Control
(SPC), have been widely implemented in manufacturing industries as an effective approach …

This article proposes a new graphical tool, the magnitude-shape (MS) plot, for visualizing
both the magnitude and shape outlyingness of multivariate functional data. The proposed …

The direction of outlyingness is crucial to describing the centrality of multivariate functional
data. Motivated by this idea, classical depth is generalized to directional outlyingness for …

Outlier detection is an integral component of statistical modelling and estimation. For high-
dimensional data, classical methods based on the Mahalanobis distance are usually not …

We apply the tensor train (TT) decomposition to construct the tensor product polynomial
chaos expansion (PCE) of a random field, to solve the stochastic elliptic diffusion PDE with …

Although several works have been proposed for multi-channel profile monitoring, two
additional challenges are yet to be addressed:(i) how to model complex correlations of multi …

We propose a new family of depth measures called the elastic depths that can be used to
greatly improve shape anomaly detection in functional data. Shape anomalies are functions …