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Using statistical shape theory for the monitoring of nonlinear profiles
Author(s) -
Cano Javier,
Moguerza Javier M.,
Psarakis Stelios,
Yannacopoulos Athanasios N.
Publication year - 2014
Publication title -
applied stochastic models in business and industry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.413
H-Index - 40
eISSN - 1526-4025
pISSN - 1524-1904
DOI - 10.1002/asmb.2059
Subject(s) - nonparametric statistics , metric (unit) , parametric statistics , nonlinear system , property (philosophy) , computer science , mathematical optimization , process (computing) , focus (optics) , mathematics , variable (mathematics) , parametric model , product (mathematics) , quality (philosophy) , point (geometry) , algorithm , econometrics , statistics , mathematical analysis , engineering , philosophy , operations management , operating system , physics , geometry , optics , epistemology , quantum mechanics
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.