Online monitoring of profiles via RVC model with an application to industrial busbar

Profile monitoring is used to check the stability of the functional relationship of the process response on several predictors. In most of the existing literature, the monitored functional relationship usually involves only one covariate and the coefficient of the covariate is assumed to be constant. In some applications, the process response depends on multiple covariates, and the functional relationship is not constant but dynamic over time, which is different from those studied in the literature. To implement profile monitoring in these applications, a semiparametric random time-varying coefficient model is employed to characterize this dynamic relationship over time. Based on this model, a profile monitoring scheme integrated with dynamic probability control limits is proposed, which can adapt to the case of the within-profile autocorrelation and arbitrary design points. In Phase I, this paper uses a backfitting iterative procedure with the REML-Based EM-Algorithm to estimate the model. In Phase II, an exponentially weighted moving average scheme on residuals with dynamic probability control limits is developed. The simulation results show that the proposed scheme performs better in many scenarios. Finally, an application to industrial busbar running process monitoring is given to illustrate the scheme's implementation.