Online monitoring of high-dimensional asynchronous and heterogeneous data streams for shifts in location and scale

Recent advancement of sensor technology has made it possible to monitor high-dimensional data streams in various manufacturing systems for quality improvement. However, existing monitoring schemes commonly assume that all data streams have the same sampling interval. This assumption does not always hold in practice, which poses new and unique challenges for multivariate statistical process control. In this paper, we propose a generic nonparametric monitoring framework to online monitor high-dimensional asynchronous and heterogeneous data streams, where sampling intervals of data streams are different from each other, and measurements of each data stream follow arbitrary distributions. In particular, we first propose a quantile-based nonparametric framework to monitor each data stream locally for possible shifts in both location and scale. Then, for unsampled measurements due to different sampling intervals, a compensation strategy based on the Bayesian approach is introduced. Furthermore, we develop a global monitoring scheme using the sum of top- $ r $ r local statistics, which can quickly detect a wide range of possible shifts in all directions. Simulations and case studies are conducted to evaluate the performance and demonstrate the superiority of the proposed method.