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Using statistical shape theory for the monitoring of nonlinear profiles

Using statistical shape theory for the monitoring of nonlinear profiles The quality of a process or product can be characterized by a functional relationship between a response variable and one or more explanatory variables. In this work, we develop a novel hybrid nonparametric–parametric procedure for the monitoring of nonlinear profiles, that is, realizations of a noisy nonlinear functional relationship between variables. In particular, we focus on the ‘shape’ property of profiles as a way of measuring their quality. Starting from a nonparametric reference curve, we select our model from a universe of parametric deformations of such a curve with the property of preserving certain important shape characteristics. To this aim, we design a metric based on the solution of a related optimization problem. In addition, we show that the problem is well posed from a theoretical point of view. Finally, we illustrate the performance of the proposal with numerical examples from simulated and real environments. Copyright © 2014 John Wiley & Sons, Ltd. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Stochastic Models in Business and Industry Wiley

Using statistical shape theory for the monitoring of nonlinear profiles

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References (23)

Publisher
Wiley
Copyright
Copyright © 2015 John Wiley & Sons, Ltd.
ISSN
1524-1904
eISSN
1526-4025
DOI
10.1002/asmb.2059
Publisher site
See Article on Publisher Site

Abstract

The quality of a process or product can be characterized by a functional relationship between a response variable and one or more explanatory variables. In this work, we develop a novel hybrid nonparametric–parametric procedure for the monitoring of nonlinear profiles, that is, realizations of a noisy nonlinear functional relationship between variables. In particular, we focus on the ‘shape’ property of profiles as a way of measuring their quality. Starting from a nonparametric reference curve, we select our model from a universe of parametric deformations of such a curve with the property of preserving certain important shape characteristics. To this aim, we design a metric based on the solution of a related optimization problem. In addition, we show that the problem is well posed from a theoretical point of view. Finally, we illustrate the performance of the proposal with numerical examples from simulated and real environments. Copyright © 2014 John Wiley & Sons, Ltd.

Journal

Applied Stochastic Models in Business and IndustryWiley

Published: Mar 1, 2015

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