Higher levels of automation in manufacturing industries are leading to data sets increasing in size and dimension. Some of this data is generated in the form of curves, also called functional observations. This talk will focus on models for such data, with emphasis on techniques appropriate for process monitoring. Two kinds of functional models will be considered. First, we consider a mixed effects model that can be used to characterize part-to-part variation in the functional data. The idea of process monitoring of random effects is introduced, which appears novel in the process control literature. In the second part, a Bayesian hierarchical model is used to cluster low-dimensional summaries of the curves into meaningful groups. The belief is that the clusters correspond to distinct types of processes and/or changes over time, and subsequent new observations can be classified as such by calculating probabilities of belonging to each cluster. The models are illustrated using both real and synthetic data. This work is based on the thesis research of University of Waterloo Ph.D. candidate Sofia Mosesova.
Group for Research in Decision Analysis