A Generic Online Nonparametric Monitoring and Sampling Strategy for High-Dimensional Heterogeneous Processes

With the rapid advancement of in-process measurements and sensor technology driven by zero-defect manufacturing applications, high-dimensional heterogeneous processes that continuously collect distinct physical characteristics frequently appear in modern industries. Such large-volume high-dimensional data place a heavy demand on data collection, transmission, and analysis in practice. Thus, practitioners often need to decide which informative data streams to observe given the resource constraints at each data acquisition time, which poses significant challenges for multivariate statistical process control and quality improvement. In this article, we propose a generic online nonparametric monitoring and sampling scheme to quickly detect mean shifts occurring in heterogeneous processes when only partial observations are available at each acquisition time. Our innovative idea is to seamlessly integrate the Thompson sampling (TS) algorithm with a quantile-based nonparametric cumulative sum (CUSUM) procedure to construct local statistics of all data streams based on the partially observed data. Furthermore, we develop a global monitoring scheme of using the sum of top-r local statistics, which can quickly detect a wide range of possible mean shifts. Tailored to monitoring the heterogeneous data streams, the proposed method balances between exploration that searches unobserved data streams for possible mean shifts and exploitation that focuses on highly suspicious data streams for quick shift detection. Both simulations and a case study are comprehensively conducted to evaluate the performance and demonstrate the superiority of the proposed method.