Using statistical shape theory for the monitoring of nonlinear profiles | Zendy

Cano Javier | Zendy; Moguerza Javier M. | Zendy; Psarakis Stelios | Zendy; Yannacopoulos Athanasios N. | Zendy

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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.

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