In-profile monitoring on univariate profile with application to industrial busbar

In the current research on profile monitoring, most studies treat each profile as a whole to design the monitoring statistic. These monitoring methods can only detect whether there exist some anomalies in the process after a complete profile sample is collected. This leads to a lag between the occurrence of a shift and the signaling of an alarm, which hinders engineers from promptly intervening in the out-of-control process. To address this limitation, an in-profile monitoring scheme is proposed in this article, in which the dynamic influence mechanism of covariates on the response variable is considered. In phase-I, a random varying-coefficient model is utilized to model the dynamic time-varying relationship between covariates and the response variable, and the model parameters are estimated. In Phase-II, for the sequential observations generated by the monitored process, a new monitoring scheme based on the generalized likelihood ratio test is designed. This scheme can adapt to within-profile autocorrelation and arbitrary design points. To enhance online computational efficiency, recursive formulas for calculating the charting statistic are developed. Numerical studies demonstrate that the proposed scheme exhibits a satisfactory and robust monitoring performance. Finally, an application to industrial busbar running process monitoring is given to demonstrate the implementation of the scheme.