Bounding uncertainty in functional data: A case study

Abstract

Functional data are fast becoming a preeminent source of information across a wide range of industries. A particularly challenging aspect of functional data is bounding uncertainty. In this unique case study, we present our attempts at creating bounding functions for selected applications at Sandia National Laboratories (SNL). The first attempt involved a simple extension of functional principal component analysis (fPCA) to incorporate covariates. Though this method was straightforward, the extension was plagued by poor coverage accuracy for the bounding curve. This led to a second attempt utilizing elastic methodology which yielded more accurate coverage at the cost of more complexity.

Keywords:

• Functional data analysis
• functional principal components
• reliability specifications
• tolerance bounds
• uncertainty quantification

Acknowledgments

The authors would like to thank Thomas Buchheit, Shahed Reza, Biliana Paskaleva and Andrew Sandoval for their contribution to the Zener diode work. The authors would also like to thank two anonymous reviewers for their helpful comments in improving the article.

Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DENA0003525.

This article describes objective technical results and analysis. Any subjective views or opinions that might be expressed in the article do not necessarily represent the views of the U.S. Department of Energy or the United States Government.

Notes

1 MATLAB code is also available at https://github.com/jdtuck/fdaSRSF_MATLAB.

2 Mathematical proof provided in Srivastava and Klassen (2016).

Additional information

Notes on contributors

Caleb King

Caleb King is a Research Statistician Developer for the Design of Experiments platform in JMP Software. Prior to working at JMP, he worked for 3 years as a Statistical Scientist at Sandia National Laboratories. He received his BS in Mathematics and Statistics from Calvin University in 2009 and his MS and PhD in Statistics in 2011 and 2015 from Virginia Tech. His research interests include design of experiments, reliability, accelerated testing, and small-sample theory.

Nevin Martin

Nevin Martin is a former Member of the Technical Staff in the Statistical Sciences department. She received a BS degree in Finance from the University of Arizona and a MS degree in Statistics from the University of New Mexico in 2010 and 2016, respectively. Her research interests include design of experiment and uncertainty quantification (UQ) methods for computer simulations, functional data analysis, statistical computing and machine learning.

James Derek Tucker

James Derek Tucker is a Principal Member of the Technical Staff at Sandia National Laboratories. He received his BS in Electrical Engineering Cum Laude and MS in Electrical Engineering from Colorado State University in 2007 and 2009, respectively. In 2014 he received the PhD. degree in Statistics from Florida State University in Tallahassee, FL under the co-advisement of Dr. Anuj Srivastava and Dr. Wei Wu. He currently is leading research projects in the area of satellite image registration and point processes modeling for monitory applications. His research is focused on pattern theoretic approaches to problems in image analysis, computer vision, signal processing, and functional data analysis. In 2017, he received the Director of National Intelligence Team Award for his contributions to the Signal Location in Complex Environments (SLiCE) team.