176 – Functional Data Analysis and Extensions to Manifold Learning
Functional Statistical Process Control Using Elastic Methods
J. Derek Tucker
Sandia National Laboratories
he problem of statistical analysis and modeling of data in process control is important in determining when a production has moved beyond a baseline. Recently, the use of functional data has become an interest in statistical process control. The observations here are time samples of real-valued functions on an observation interval, and to perform effective data analysis it is desirable to have a generative, probabilistic model for these observations. The model is expected to properly and parsimoniously characterize the nature and variability in the baseline data. It should also lead to efficient procedures for conducting hypothesis tests, performing bootstraps, and making decisions. We wish to perform statistical process control (SPC) using functional data. We present a technique that takes into account both amplitude and phase variability in the data using the square-root slope framework. In this work we present metrics that are defined to measure both types of variability and show demonstration when the data has gone beyond the control limits.