• adaptive Neyman test statistic;
  • autoregressive models;
  • discrete Fourier transform;
  • multivariate statistical process control;
  • profile data;
  • time series models


Profile monitoring is an important and rapidly emerging area of statistical process control. In many industries, the quality of processes or products can be characterized by a profile that describes a relationship or a function between a response variable and one or more independent variables. A change in the profile relationship can indicate a change in the quality characteristic of the process or product and, therefore, needs to be monitored for control purposes. We propose a high-dimensional (HD) control chart approach for profile monitoring that is based on the adaptive Neyman test statistic for the coefficients of discrete Fourier transform of profiles. We investigate both linear and nonlinear profiles, and we study the robustness of the HD control chart for monitoring profiles with stationary noise. We apply our control chart to monitor the process of nonlinear woodboard vertical density profile data of Walker and Wright (J. Qual. Technol. 2002; 34:118–129) and compare the results with those presented in Williams et al. (Qual. Reliab. Eng. Int. 2007; to appear). Copyright © 2010 John Wiley & Sons, Ltd.