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Due to rapid developments in technology, profile monitoring is becoming challenging, as the profile data are a series of observations on a specific quality characteristic that are taken across some continuum. In this paper, a functional exponentially weighted moving average (FEWMA) control chart is developed for phase-II monitoring of nonlinear profiles based on the functional data approach. In particular, the profiles are estimated using cubic B-splines to solve the problem of high dimensionality that hinders the implementation of classical multivariate control charts. An extensive simulation study has been conducted to validate the effectiveness of the proposed control scheme for detecting changes in the functional mean of the process to its magnitude and assuming scenarios of independence and dependence between curves. The properties of the run-length distribution of the proposed scheme are discussed. The FEWMA control chart is also applied to the real-time data of the vertical density profile of particleboard manufacturing.
Naeem et al. (Mon,) studied this question.