Kernel-based control charts for monitoring functional nonparametric regression processes

In statistical process control (SPC), considerable effort has been devoted to monitoring process characteristics after adjusting for the effects of additional covariate information. Traditional approaches typically incorporate regression models into monitoring frameworks under the assumptions of scalar covariates and prespecified parametric relationships. However, many modern applications involve more complex settings in which covariates are inherently function-valued and the covariate-response relationship is nonparametric. To address this issue, this work develops a residual-based exponentially weighted moving average (EWMA) charting scheme for functional nonparametric regression processes. The proposed method is built upon a reproducing kernel Hilbert space (RKHS)-based regression framework, which accommodates infinite-dimensional covariate structures without imposing explicit parametric forms. Extensive simulation studies demonstrate that the RKHS-based chart achieves consistently higher sensitivity to location shifts than several existing monitoring methods. A case study based on a food-industry spectrometry dataset further illustrates the practical applicability and versatility of the proposed approach.