Distribution-free multivariate time-series monitoring with analytically determined control limits
提出一种无需模型拟合或试错校准控制限的多变量时间序列均值漂移检测方法，通过将观测向量转化为一维T2量并构建CUSUM统计量，利用反射布朗运动解析确定控制限，适用于多种相关结构的数据。
We consider the problem of detecting a shift in the mean of a multivariate time-series process with general marginal distributions and general cross- and auto-correlation structures. We propose a distribution-free monitoring procedure that does not need model fitting or trial-and-error calibration for control limits, which makes the procedure convenient to be implemented when a facility consists of many processes to be monitored. The main idea is to convert each observation vector into a one-dimensional $ T^2 $ T2 quantity that captures cross-correlation. The $ T^2 $ T2 quantities form a univariate auto-correlated process, and CUSUM statistics are constructed on the $ T^2 $ T2 quantities. Then using the fact that the CUSUM statistics on the auto-correlated process behave as a reflected Brownian motion asymptotically under some conditions, the control limits of the CUSUM procedure are analytically determined by setting the first-passage time of the Brownian motion equal to a target in-control average run length. We compare the performance of our procedure with three competing procedures on simulated data with various cross- and auto-correlation and real data from a wafer etching process. The proposed procedure delivers actual in-control average run lengths close to the target and shows comparable or better performance in detecting a shift in mean than the competitors.