  In modern manufacturing, most of the product lines are conforming. Few
products are nonconforming but with different defect types. The identification
of defect types can help further root cause diagnosis of production lines. With
the sensing development, signals of process variables can be collected in high
resolution, which can be regarded as multichannel functional data. They have
abundant information to characterize the process and help identify the defect
types. Motivated by a real example from the pipe tightening process, we focus
on defect classification where each sample is a multichannel functional data.
However, the available samples for each defect type are limited and imbalanced.
Moreover, the functions are incomplete since the pre-tightening process before
the pipe tightening process is unobserved. To classify the defect samples based
on imbalanced, multichannel, and incomplete functional data is very important
but challenging. Thus, we propose an innovative classification framework based
on deep metric learning using functional data (DeepFunction). The framework
leverages the power of deep metric learning to train on imbalanced datasets. A
neural network specially crafted for processing functional data is also
proposed to handle multichannel and incomplete functional data. The results
from a real-world case study demonstrate the superior accuracy of our framework
when compared to existing benchmarks.
