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 (c) 2014 John Wiley & Sons, Ltd.