Risk adjustment-based statistical control charts with a functional covariate

In real applications, there are situations in which quality characteristics are significantly affected by function-valued covariates such as electrocardiogram (ECG) signals; however, previous surveillance methods with covariate adjustment mainly use scalar-valued covariates to construct control charts to investigate the stability of nonindustrial processes, such as in the medical and public health fields. Few existing approaches address the infinite-dimensional regression encountered with function-valued covariates. Thus, an applicable scheme needs to be developed. Here, by relaxing the assumption of normality, a novel surveillance strategy for functional logistic regression (FLR) is proposed. In this approach, the response is a binary variable, and the covariate information is obtained from functional data. To address the above problems, functional principal component analysis (FPCA) is used to extend the score test to situations with functional covariates. Moreover, the score statistic is integrated into an exponentially weighted moving average (EWMA) charting scheme to detect abnormal changes in the location and scale parameters based on additional information. The simulation results show that the proposed approach is more efficient than previous approaches in detecting small to moderate shifts. Finally, the proposed charting scheme is applied to a real case study to demonstrate its utility and applicability.