Online nonparametric monitoring for asynchronous processes with serial correlation

Existing multivariate statistical process control methods commonly require all data streams have the same sampling interval. In practice, this assumption may not be valid, as different sensors can have different sampling intervals. In this article, we first propose a generic nonparametric monitoring scheme to online monitor the asynchronous data streams without considering serial correlation. Then the proposed scheme is extended such that it can handle serially correlated data streams. Specifically, we construct a nonparametric local statistic for each data stream, which is sensitive to mean shifts. To eliminate the influence of different sampling intervals, our innovative idea is to transform the local statistics into time-related statistics according to the sampling intervals. A global monitoring scheme is then constructed based on the sum of top-r time-related statistics. To extend the proposed method for serially correlated data streams, we further propose a novel estimation method for the pairwise covariance functions and the data streams can be decorrelated accordingly. Numerical simulations and a case study are conducted, showing the effectiveness of the proposed method in handling asynchronous data streams with serial correlation.