Using statistical shape theory for the monitoring of nonlinear profiles

Javier Cano, Javier M. Moguerza, Stelios Psarakis and Athanasios N. Yannacopoulos

Applied Stochastic Models in Business and Industry, 2015, vol. 31, issue 2, 160-177

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.

Date: 2015
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https://doi.org/10.1002/asmb.2059

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Persistent link: https://EconPapers.repec.org/RePEc:wly:apsmbi:v:31:y:2015:i:2:p:160-177

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